 Good evening guys. Good evening. Good evening. Good evening. Good evening. We can hear you sir. We can hear you sir. No, there was a call also so I was responding to that. Thank you very much. I could see your chart. See your chart. Okay guys. Yeah Bharat. What happened? Really fine. Don't spread this rumor that I have come for something. Not at all. Yes, yesterday there was like a tied throat or something like that. But yes, it's totally fine. Yesterday also there wasn't any cough. Okay. Oh, naffle champions are here. I thought you guys might not be here reason being your term test going on. Term like sorry like UT's unit test. Okay. Sorry. Sorry. Sorry. Okay. So 50 people here and here I am. We are talking about physics today. It's 4th of July and here we go for the first question. A is equals to this much and B is equals to this much. Then what will be the magnitude of A cross B? Relax, calculate and respond. Relax, calculate and respond. That's the beauty is you guys are calculating and responding because the speed of receiving the tsunami of responses is decreased. Good. A is given. B is given. Perform A cross B and calculate its magnitude. Yeah, naffle. I'm sorry, but because like you guys told me you will not be here. R and R did. No lies. Vector is over at R and R. Okay. No problem. No problem. No problem. No problem. No, no, no. 23 people got it right. Relax. First of all, let's learn cross product for a while. Okay. First of all, let's learn cross product for a while. How to perform cross product? Please mute. Good. Thank you. Relax, relax, relax, relax. First understand how to perform cross product because that will be required for further questions as well. Okay. Relax. Whenever there is a vector A, B, it has to be performed for cross product. You go for I, J and K. Please for R and R and naffle. Okay. I guess for naffle, I have covered a minor part of it, but it's okay. No problem. Sir, minus D. Minus D. Not here. Not required here. One, two. Okay. And two minus two and four. Okay. Then, yes, while expanding, you write I minus J plus K. Okay. So, when you calculate, when you calculate, when you calculate I, you hide the row and column associated with I. You will get the answer as 1 into 4 minus as a part of the formula minus 4. Got it? Sir, can you repeat that part again, please? Repeat, which I see. You will write I, J, K first line, coefficients of I, J and K from vector number 1, coefficients of I, J and K from vector number 2. Okay. When you have to, then you will write I minus J and K. Okay. For calculating the coefficient of I, you will hide the row and column associated with I. You will see four numbers plus square. You will cross-multiply them and subtract. So, 1 into 4 is 4 minus as a part of formula minus 2 into 2 is minus 4. G, I, got it? Right? I am only talking to, right now, I am only talking to naffle and R and R. Clear? Good. Then you want to calculate for J. Okay. What will you do? You will hide the row and column associated with J. Clear? What do you see? 3 into 4, 12 minus as a part of formula 2 into 2. Clear? No messages from, no messages from anyone excluding R and R and naffle. This is not centymar. Right now, I am teaching them something. Please do not interfere. Clear? Good. Then comes K. You will hide the row and column associated with K. What you will see? 3 into minus 2, minus 6, minus as a part of formula 2 into 1, 2. G, I, got it? My dear friends from R and R and naffle. Good. What is the answer? This is 8I minus 8J minus 8K. The answer will be 8 root 3 when it comes for magnitude. G, I, got it? Sir, can you calculate the magnitude once? 8 square plus 8 square plus 8 square square root of 3 times of 8 square. So, it will be 8 root 3. Yeah, yeah, okay, got it. Okay? Yeah. Mintro got my root. Okay. So, everyone got it? Ready? So, now guys, throughout this session, wherever the cross product has to be performed, this is going to be the method. Okay, naffle and R and R. Okay? Good. This is the shorter method. Okay? So, let's look at the leaderboard for 23 people. Sir, today only cross product or even dot product? 1 or 2 questions might be there. For dot product as well, whenever it will be required, it will be thoroughly mentioned. Abhishek is the fastest one. Siddharth is there. Avni Anvi is there. Okay? Pratham, Jagrap, Himanshu, Dhruv, Srijan, Gandhar and Crocodile. Good. Here we go to the next question. Next question is an instruction. Read that. Or also called as moment. Or also called as moment of force. Or also called as rotational force or turning effect is the rotational equivalent of linear force. Okay? Mathematically, torque is equal to the cross product of vector and force. Clear? Vector of position, that is position vector and force. Got it? What is the formula noted? That torque wherever as cross product. Yes, please, please, please. Sir, what do you mean cross product of position vector and force? Isn't it like, so is force also going to be a vector? Force is a vector, no? Okay, fine. Good. Force is mass into acceleration. Acceleration is a vector, mass is a scalar. Okay? Good, good, good, good. Only 40 people marked it. Whereas we have minimum 50 people there. May I proceed? The torque of the force F is given acting at the point R is given about the origin B. You know what has to be done. The previous statement was the hint, was the knowledge, was the concept required for it. Good. Guys, relax and respond. 48 people have responded to this. So for this you only, so you just needed to do like, you could just like find which is the correct answer just by getting the first value of I. Good, very good. See, what my dear friend just now said, he said this was the definition. Okay, now this is the question. If you'll check, you don't have to save a time is a secondary thing. What he said, he said in order to save time, why are you calculating all? Because all are distinct, just calculate anyone, yes or no? Right? So it's D, can you fix it? No, repeat. So the answer is D. Sir, it is D. Bravo, Charlie or Delta? Delta. Sir, Delta. Claps, claps, claps. Look at the definition, my dear friends. It's position vector into force. Now look here, what have you guys done? Got your mistake? Yes, I will solve it up by the very definition which we just now learned. Torque is... Sir, I don't get it. Yes or no? The definition which we learned now. Torque is R cross L, yes or no? Relax guys, see, this is the definition, right? What is torque? Torque is position vector multiplied with force. Okay, here it is, position vector multiplied with force. Now what my dear friends suggested, he said, why are we calculating all? We can just calculate one and get the answer, right? Okay, so he said sir, okay. Anyway, if someone want to perform, they can perform the whole product, but I am not going to do that. Got it? I am going to comprehensively solve, I am solving comprehensively here. I, J, K. R, 3, 2, 3, F, 2 minus 3, 2, right? Again same thing, just for I, I will have 8 minus minus 9 which is 17 I. I have my answer. Got it? 11 people, mild bravo, no problem. Monisha, what happened bitter and mutant talk to me? So in cross product from this observation, I can tell if we switch the thing, if we do F cross R, then becomes minus 1 into R cross F. Exactly, got it? Okay. Yeah, so if you, yeah exactly, good, good, good, good, good. If you remember while discussing also, we have stated it, A cross B is equal to minus of B cross A. What is the proof of it? I will tell you. This I, J, K is the proof of it. If you will do I into J, you will get K, but if you will do J into I, you will get minus K. Yes or no? Got it everyone? Got it? Got it? Got it? Good, good, good, good, good. Be aware, be alert, okay? So read it properly. That's why I have kept 10 questions only. Sure? Clear? R for ready everyone? My R and R friends and my NAPL friends, okay? Sure. Leaderboard, Jagra, Himanshu, Namrata, Prateek and yes, very good, very good, very good. Sure? Here we go to the next one. A cross B is equal to C. Then which of the following statement is wrong? Wrong statement. Good, good, very good, relax, relax. Good Aditya, Raghav Pandey, very good. No problem, Nishant, no problem. Raghav is so impatient. No problem guys, relax, relax. The definition of cross product is the answer. Everyone has voted, very good, very good. Oh, look here. No problem guys, no problem. Relax C. The definition of cross product says the A cross B will be equal to magnitude of A multiplied with magnitude of B multiplied with sin theta and the unit vector which is mutually perpendicular to both, mutually perpendicular to both A and B. That means whatever comes as an outcome, please note, please note whatever comes as an output of a cross product between two vectors that output is mutually perpendicular to both. That way it will be perpendicular to A, it will be perpendicular to B. Sure, hence it will be perpendicular to A plus B as well. Yes, it will be parallel to A cross B. Okay, sure, by A cross B is nothing but sin, you could have just replaced the value. The answer is C cannot be perpendicular to C. Okay, G, I, got it? Very good, very good, relax, very good, relax, very good. One, two and next. The lead board. Nisrat is now answering it. You had to just substitute. Pratam was the fastest one to respond. Very good Pratam. And here we go to the next question. If for two vectors A and B, A cross B is zero. The vectors are perpendicular, are parallel, are at 60 degree, are at 30 degree. The vectors are perpendicular, parallel, 60 degree, are at 30 degree. Very good, very good. What was the definition just now is the answer for it. If you know a single term in the definition, you have the answer. Relax, relax, relax, good. 41 people have answered by now, 42, 43, 44, 45, 46. Good, good, good, good, good, good, good, good, good. Good, Ruthvik. Good, Siddharth, no problem. Why so much time for this question? Because I know my dear friends will need the time. See, everyone hasn't voted yet. Now they have voted and yes, we have 14, 35, 5 and 1. 35 people answering it very right because if A cross B is equals to zero, this implies that sin theta is equal to zero and theta equal to zero degree. That means they are parallel. Gi, got it? Simple. If dot product is equals to zero, implies that perpendicular. Cross product equal to zero implies that parallel or anti-parallel. It can be anti-parallel as well. Yeah, good, good, good. So let's look at the Shuffle leaderboard. So yes, yes, yes, yes, yes, yes. Himanshu, Jagrav, Nitin, Anuya, Aditya. Anuya was the fastest one to respond very good. And here we go to the next question. Angle between the vectors A cross B and B cross A is. A cross B and B cross A. The hint was there in the previous solution. Previous solution. A cross B and B. So someone even said this, said this out in that question where I had said you could use the shortcut method. Yeah. I told you the last, the last, the last solution was a straight hint. Let's see who all like it. 53 people, 2 more people yet to answer. Time up. Everyone has voted good. Oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, guys please. I'm shocked. I'm in terrible shock, guys. You know from the first question, from the last question that A cross B is equal to minus, please right they are in opposite direction if they would have been in same direction then zero but they are in opposite direction so 180 relax guys no not this it's not a class mute yourself so I'm slightly confused I don't know relax no problem so relax relax relax how many of you got this line accepted this is very well accepted right very well accepted so and you are also clear that whenever there are two opposite vectors their angle between them is 180 degree so clear yeah good now okay please understand if yeah there are two vectors at zero and you have to round them to 180 degree you cover a semicircle a semicircle is pi into radius so you call it pi for a full circle you have to rotate it two pi two pi two pi is 360 degree and pi is 180 degree if you are not aware about this I'm sorry I'm sorry I'm sorry so so Tushaso was teaching his sister exactly exactly I'm radian yeah this has been covered better indirectly might not be directly but many a times indirectly this information has been delivered so now you are the new trap king I am not the trap king I can't be the trap king my each solution is related to the next question you know I arrange the question very systematically could you do it once more yes please see then understand this nothing when you wrote complete a circle right or not then you cover 360 degree okay and in that case you covered yes okay that is 360 into r so two pi is 360 degree our pi is 180 degree got it okay yes got it good very good very good very good no problem no problem no problem and now Jagra very good very good Raghav was the fastest one to respond no problem no problem no problem here we go to the next question what is the unit vector perpendicular to the following vectors now if you remember two questions back there was a solution for this in the explanation you had the solution for this what is the unit vector perpendicular to the following vectors is there general awareness tomorrow sir but I am not aware about it but okay if there will be the child I will write down to you okay so I realized after solving that all the denominators are the same why sir why did you put all the denominators as the same as I solved it it could have saved me 20 seconds unsure about denominator but there is no surety required for denominator so 10 11 23 positive positive sign very positive sign very positive sign so yes here while explaining this here while going through this we like to this to this and all we mean through the concept that that the cross product did not take my answer repeat sir it did not take my answer I clicked on see he did not take it it said you didn't vote in time sorry which is like I literally can't help you with this because it's done okay sorry let's see if it repeats then we look for a solution okay two two minus one six minus three j now understand again the same method you can opt for again the same method you cannot opt for again the same method you can opt for what so you didn't need to calculate i or the denominator what you want to calculate there i have only jnk only jnk good good good good good good now i have a reverse solution for it should i suggest you that the reverse solution yes you know reverse solution i am telling you a reverse solution if your brain is working in complete verticals of vector then you know the answer will be perpendicular to both of them yes or no so the dot product which is very easy to calculate should be zero only if only if i don't want you i don't want to insist this right but yes if i would have been at your place my approach to save a time would have been to buy all these are the cross product of these okay that means a cross product which we just saw at sea should be perpendicular to this one should be perpendicular to this one or both and all that right so what i'll do i'll do the dot product with any of them and we'll find whenever the dot product is coming to zero will be my answer gi got it or not because dot product is way easier to perform than cross product it's lengthy cross product is lengthy also and complicated also whereas dot product is just a bacha thing right and you can see my answer is there yes or no this is see this is coming out as 2 plus 20 plus 18 oh if this would have been minus will would have been a lottery okay change the sign charlie is the answer 10 seconds gi got it or not now let's do it formally the way we are conducting this let's do it formally let it take some time no problem so what we will do by fine cross product of these okay so i j k 2 2 minus 1 6 minus 3 into 2 okay for example i calculated i what i'll have have just for you guys i'll have 4 minus 3 which is 1 okay so here but the problem is there is no requirement of calculation of i why because it's same everywhere right let's go for j okay j will be 4 minus minus 6 okay okay okay with a negative sign so it is minus 10 which is which is available either at bravo or at charlie yes or no clear till here now let's go for k minus 6 minus 12 minus 18 which is here charlie is the answer got it huh beta if you remember the process i told you i into minus j into plus k right huh see beta what answer you are getting is not a unit vector in order to make it a unit vector you will have to divide the vector by its own magnitude right tanya yeah yeah yeah so no problem no problem no problem let's go for the leader board jagrav heman shoe no heman shoe is not there jagrav was the fastest one to respond very good jagrav excellent here we go to the next one what what if a cross b is equal to root three times of a dot b then the value of magnitude of a plus b is i have taken it long to the revision long to the revision relax read and respond to only look at one particular part of the answers that will be there simple what you guys need for this question are the remembering or the memory of the values of sine cos and tap sine 0 30 45 60 90 cos 0 30 45 60 90 tan 0 30 45 60 90 okay is that t by f i couldn't understand better than we okay that's a true or false no no there isn't any true or false only 13 people got it right relax guys read concentrate read see if you expand this you will get a into b into sine theta if you expand this you will get root three a into b into cos theta a b a b got cancelled you have tan theta equal to root three that means theta equal to 60 degree yes or no yes or no yes or no okay sure now what i was saying you have to only look at the part of the addition where theta is involved a square b square a square b square is not plus 2 a b cos theta what is cos 60 degree 1 by 2 2 and 2 got cancelled only a b should be there which is there in delta g i got it okay i repeat by this you got that theta is equal to 60 degree okay in the addition theta is involved as the third part 2 a b cos theta which is 2 a b 1 by 2 cancelled only a b should be visible okay delta is the answer g i okay shivam no problem look at the leadboard very good jagra very good shri jen very good shri ram very good pratik tanvi siddharth was the fastest one to respond very good siddharth here we go to the next question read it read the instructions carefully don't give a thumbs up without reading it please when a force causes a body to move work is being done on the object by the force okay so work is measure of energy transferred when a force moves an object through a distance d okay when work is done energy has been transferred from one energy store to another okay energy transferred is equal to work done mathematically most of you will be like sir i have this mathematically work is the dot product of force and displacement vector good i am waiting for everyone to read it good post reading you have to give a thumbs up at the down like at the side sorry good good good good good good good good good okay i shouldn't have mentioned that dot word yeah i'm waiting so if you if you hadn't mentioned the dot i won't have seen it okay thank you when everyone respond i'll go see no problem okay are for ready everyone so how many more questions are there two more bitter here we go a force f acting on a particle causes a displacement s in its own direction if the work done is 6th june then the value of c will be relax okay see work done has to be calculated work done is given as six so the dot product should be equal to six do the dot product between these two vectors what happens if that relax good you guys are spending time that's beautiful to look at very good shivam very good very good so motivating but relax relax this is a definition now here the dot product is minus 12 plus 2c minus 6 is given as 6 okay 2c equal to 24 c equal to 12 got it everyone everyone got it good very good very good monisha monisha what happened again better work done is defined as force into displacement dot word okay so okay let's perform the dot product between these two vectors here displacement is given force is given 3 into 4 is minus 12 c into 2 is plus 2c 2 into minus 3 is minus 6 equal to 6 is what is given okay yeah good this is coming as 2c equal to 24 c equal to 12 got it everyone got it got it got it got it got it got it got it got it very very very good very good very good leaderboard okay now we'll have a shuffle but no because the gap was high very good very good very good very good very good very good aditya was the fastest one to respond very good here we go to the next question jagarov good a force f is applied over a particle which displaces it from origin original position to the point s is equals to this the work done on the particle is the work done on the particle is the work done on the particle is what happens there there is a trap but easy to cross easy to cross you can consider there's a trap the trap is just only to let you think to like delay your response time by some 3 4 seconds okay good right work done is just the dot product 5 2s are 10 3 into minus 1 is minus 3 plus 7 I just kept this minus 7 so that you will spend some time to think oops like that okay yeah good good very good very good next question good good good good good good good good good good good good good shri ghan was the fastest one minor difference of 100 plus points between shri ghan and jagarov very good shri ram is also there raghava is also there and here we go to the last question last question last question last question last question last question is just there to give you a relief but if you guys remember last question is the first question of the last quiz that's what you call the word trap now I'll get who all remembers what is happening in the class this question which is last question for today's quiz was the first question of the last quiz no better throw I want to but not getting time and not like literally I want to like I want to sit down you hate me thank you a chair thanks a lot and people got it right and you know as the response of a cross product is a vector it should be zero vector let's see the scenario damn you shri ghan nice competition yeah healthy competition healthy wow shri ghan like played really well wow jagarov very good very good very very excellent jagarov shri ghan very excellent healthy game very good very good very good nice everyone good anyway as I always say these all things are the garnish thing the cult the core thing is the learning which is coming out of you can hate me for it okay you can just take it for granted but if you remember the learning outcome of this one hour that is fairly enough for the efforts being put to create them thank you very much guys thanks a lot good night see you next week bye bye thank you sir thank you sir thank you sir amazing quiz amazing quiz myself thank you sir thank you a chair bye bye