 make it quite late. Thank you and oh 22 and 22 scenario scenario why because cross product is a zero vector vector cross product is a vector product your outcomes will be vector your outcome is zero but not just a normal zero a zero vector G I got it no confusion moving on to the next question before that looking at the first entry of the leaderboard okay the fastest friend of mine was Tony good and here we go to the next question then a dot b is equal to negative of a and b then the same thing you got got similar number negative one the camon attended those who attended came on seriously and understood its solution and explanations will have a good answer right you are actually and sincerely looking for negative one good good good good good good relax I want to see that everyone has responded no problem Aditya relax took time but got it good very good number and times over now we have the results nineteen four four look here my dear friends a dot b is equal to negative magnitude of a magnitude of b by the very definition of a dot b by the very definition of a dot b we got that negative one is equals to cost theta for this and cost is negative one when theta is equals to 180 degree and when two vectors are 180 degree they are opposite to each other G I got it yes in radiant measure format 180 can also be stated as by good moving on to the next one Pooja Parth Karun Raghav Harsh Rishi Shivam Harsh being the fastest responder and as of now leading the scenarios and here we go to the next question no problem Onisha dot product of two mutually perpendicular vector is dot product of two mutually perpendicular vector mutually perpendicular vector mutually perpendicular vector mutually perpendicular vector just trying to confuse my dear friends like sometime sometime like just confusing people is really good really really good sir it is still stuck in that answer fast to get more points page repeat sir it is still stuck in that previous page before the question the answer fast to get more points that page is still stuck in that page okay but I am parallel you see this that might be just at your end because I am parallel receiving and witnessing the whole presentation over my phone because there I am responding to the charts as well right so please refresh with it that's the only solution I can give as of now and time's up people answered and they answered it right exactly by dot product of two mutually perpendicular vectors perpendicular vectors means that the angle between them is 90 degree cost of 90 degree is 0 hence everything their magnitude etc will become 0 answer is 0 no 0 vector the reason being dot product is a scalar product okay good moving on to the leaderboard 40 people answered it right so now we are going to have a good beautiful shuffle yes someone speaking please repeat okay Nishant was the fastest one to respond very good very good very good yes cross product is dependent on the sign whereas dot product is dependent on the cost and here we go to the next question if A and B are perpendicular vectors and vector A is given and vector B is given then the value of A is then the value of A is 11 people have answered by now very good still one whole big chunk of the time remain the previous question is an hint to this question good good good good good good good 31 people answered it by now no problem continue play with all the patients so that okay got it got it number the very good very good very good relax the sign the sign yeah exactly I guess my dear friend someone in you I went through that over the messages over the chat that someone said he said signs are messing up like little yeah and yes time up everyone has voted looks beautiful but boom right relax right relax A dot B is a 5 into 2 10 7 into 2 40 minus 3 into minus a plus 3 this has to be 0 so a should be minus 8 dot product of A and B right 5 like I will get multiplied with I 5 into 2 10 J with get multiplied with J 7 into 2 14 K with get multiplied with K minus 3 into minus a will be plus 3 this is 24 being transferred here 3 a is equals to negative 24 a is equals to negative 8 okay no problem here no problem relax relax relax relax relax 20 people answered it right 23 people a big big chunk and here we go to the leaderboard Bharat no at this point of the day no that stock sec puja good good good and here we go to the next question good Namrata very good the position vector of points a b c and d are a b c and b then the displacement vectors a b and c d are perpendicular parallel antipalm inclined at an angle of 60 degree relax read and response how you did you get it right or wrong 22.992 seconds to answer please please don't mess in calculating the displacement vectors the first thing you have to calculate the displacement vectors they are not given good good great good no problem no problem relax good Ashish no problem bte 40 seconds plus got it roughly that's way more than a good achievement okay okay Monisha sooner in five more seconds this help will reach out to you and let's see 24 12 goddess hmm relax I told you don't mess up while calculating don't mess up while calculating the displacements to be in the translate sorry sorry sorry a to be is four minus three one five minus four one six minus five one this is going from a to b as stated here point number one gi point number two cd four minus seven minus three six minus nine minus three zero minus three minus three they are proportional but in opposite direction parallel no antipalm yes gi got it I didn't get your last statement like so why did you tell again how you calculated the displacement yes Peter yes yes yes yes going from a to b final minus initial final minus initial final minus initial got it similarly going from C to D I told you I gave you a hint don't mess up while calculating the displacement final is the final minus initial minus three final minus initial 0 minus 3 minus 3 gi got it now reaching out to the last statement concludes but they are proportional 1 by minus 3 is equal to 1 by minus 3 is equal to 1 by 3 minus 3 even upon a 2 is equals to b 1 upon b 2 is equal to c 1 upon c 2 they are parallel but in opposite direction beta they are called antiparallel gi got it if not make a note of it beta that will be surely helping you out so say if like the top and the bottom are not equal then it's antiparallel like opposite direction no beta sign sign sign oh suppose this would have been 3 3 3 then they are parallel okay oh okay okay got it okay good good 12 people only so there will be a good magnitude of shuffle yes see Arushi Sanjana Yukti fish my dear friend Tony Arushi is on the leaderboard top Tony was the fastest one to respond good and here we go to the next question angle between the vectors i plus j j minus k is you have the formula for angle between the vectors don't get impatient apply the formula get the answer you will feel good you will really feel good miss clear nitya no problem easy Krishna good very good namrata easy good so let at least for this question i want to see that everyone has responded at least 10 seconds before the time if it is easy if you feel it's not easy please concentrate read and respond how but mark through elimination okay that sounds better but i don't think so you can eliminate any scenario no problem Ashish very good relax yeah exactly Raghav very good clap for Raghav claps for Raghav on his face hahaha Raghav don't mind here please don't mind my laugh okay sure i hope you take it as a sport okay if you don't then please you can give me a very clear hint because i did not like it here we go for the questions relax and read you were misdirected who misdirected you Raghav angle between the vectors by the formula it will be cos theta equal to dot product divided by the individual magnitude okay dot product i into i nothing j into j 1 0 into k nothing okay magnitude square root of 1 plus 1 square root of 1 plus 1 the whole answer is 1 by 2 cos theta is 1 by 2 at 60 degree i told you don't make a hurry solve it you will feel good those who have solved they they i i can say that they really felt it good okay oh wow right i will repeat the formula for angle between two vectors is cos theta is equal to their dot product divided by their individual magnitude the product okay so what is the dot product between this vector and this z 1 i but 0 i 1 j plus 1 k 1 j sorry 0 k into minus k divided by square root of 1 square plus 1 square square root of 1 square plus 1 square got it yes i got confused because you said it so fast okay no problem no problem you can anyway just put a hump in front of me because there are no speed breaker okay so here we go to the leaderboard monisha you wanted something there are no yay my dear friend namrata is on the leaderboard good good good anuea was the fastest one to respond very good anuea very good very good arushi is leading the show very good arushi very good very good very good here we go to the next question the vector p and q are perpendicular to each other the positive value of a is giving you a hint after 10 seconds but really happy to see only single response after 15 20 seconds this is the first time in my life i saw this dedication love you all like wow great more than 17 seconds were over and there was a single response that's really really motivating for me giving you a hint beta you will have to use quadratic equation if you'll go with splitting the middle term it will become easier that's the biggest fit i can give good good good good good good good good good good great so but camon had positive influences of my very beautiful champs right you are like taking things seriously post camona good namrata good good for everyone else as namrata has announced it over here everyone else it they are dispatched to everyone today okay good and the time's up oh oh oh oh beautiful kava 29 18 8 no problem no problem last look at the question the vectors relax monisha no problem it a vector p and q are perpendicular that means dot product of p and true will be zero let's do the dot product the dot product will look like a into a a square a into minus two minus two three into k minus right a square minus three a plus a minus three a minus three a plus one a equal to minus one and three g i got it beautiful so only the positive value and here is the answer g i got it so how do you get negative one and positive three better this has to be equal to zero right or not it's like the solution oh when the a goes you're okay yeah exactly which will go it's like that effect yes or no sign change yeah yeah got it here we go to the next question and before that a good shuffle lead board or she is still leading the scenarios my dear friend tony was the fastest one to respond very good and here we go to the next question the angle between two vectors tongue and tongue will be relax and respond relax and respond relax and respond relax and respond relax and respond i am not sure why nithya this is something to be very sure about anish misclicked no problem sir i don't know i had started doubting myself like you know nithya why whenever you are in a doubt relax best thing you can do okay if you guys have heard about the ramcharit manasa there are seven chapters right one chapter being the sundar kaan yes or no anyone like mental diagram not very reliable no so you guys haven't been through that ramcharit manasa sundar kaan and all right good chalo no one's giving even a damn about what this old man is saying and 22 people made it right good good good good good good chalo let's see now between two vectors by a dot b will be five into five i know 25 will be five into minus five i know minus 25 i know it should be divided by the magnitude and the magnitude but the beautiful numerator is giving me zero and whenever the dot product is zero the vectors are perpendicular g i got it okay monisha i am static over here sir i got log dot of of menti.com so can you just share the code once again code guys code please guys code please one four five one seven one repeat monisha good monisha c they are talking about angle between two vectors so we'll say okay we'll go for cos theta is it equal to dot product divided by their individual magnitude right or not so could you please repeat the formula for yes cos theta is dot product of the two vectors what is a dot product 25 minus divided by their individual magnitude 25 plus 25 50 25 plus 25 50 it's okay anyway the answer is zero so cos zero is f 90 degrees g i got it my dear friend who was having a discussion with me okay good so here's the scenario let's move forward aroshi missed it out karun let's see who's the fastest one to respond very good karun very good very good no problem aroshi just another question okay yes no no no need to be that sad my dear friend i fell for the trap sir no problem let's go for the next question p dot q is equals to p into q then the angle between p and q is say you say you mean magnitude of p into magnitude of q yeah exactly p into q just without an arrow mean magnitude good good good good good good good nice suggestion my dear friend whoever was there on the voice next time i should mention this is a mentionable thing good good good nice suggestion raghav okay raghav satvik relax no problem my dear friend no problem grahesh no problem tanya no problem rudra ditya guys see you guys spam a lot i really don't have any problem with spam little the only thing is our dear friends while they are sending messages okay important messages get mingled up with the majors and especially it creates a good lag right please avoid that no good good good good good and stands up let's see what's the scenario over the scores 365 114 yeah look here but it's given is 0 with 270 just for fun p dot q is pq good it should be actually p dot q should be actually p into q into cos theta oh it's not existing that means it's 1 and cos theta is 1 at 0 degree gi got it good good good good good good good i will repeat it p dot q is actually fundamentally should be magnitude of p into magnitude of q into cos theta this is p this is q okay nothing is there so cos theta is 1 cos theta is 1 at 0 degree gi got it sir why didn't you put 270 degrees instead of 0 just to make it harder just to make it harder yeah this could have been a good choice but in that scenario beta 270 won't work right 270 will not work because at 270 cosine will be 0 you know that at 0 degree 1 at 90 degree 0 at 180 degree minus a word 0 okay no problem no problem you really helped other to learn a good pattern good good good and 360 is nothing but 0 okay good good good good nice suggestion 180 won't work better for that it has to be a negative sign if you remember we had it initial questions like negative sign yeah good good good good good no problem my life mixed up my dear friend Arushi Mishank let's Karan was the fastest again very good Karan very good very good and here we go to the next question angle between the vectors again plate now there are people who had taken the burn initially so let's see how many learned from the last accident they had yes true good total how many questions I really forgot post creating no there is a minor difference but uninfluencing okay so the 13 questions yeah but some some dear friend of ours was asking whoever in top seven so your air good good good good good good performing both the ways by your action and by others good and time's up everyone has voted for this 33 people got it right it's good I was expecting a higher score but no problem oh yeah you can say oh yeah hi there between the vectors this and this again dot product i is not here 0 j is here 1 k is not here 0 by square root of 2 and square root of 2 is equal to force theta so theta is equals to 60 degree gi got it good good good leaderboard Nishant Arushi Shivam so few of the top rankers heard you my dear friend yeah exactly shijan good good good good good and here we go to the next question one more request to be thrown by you shijan the angle between two vectors is which type of pizza it is huh pi jj a that's a wrong practice lagav between two vectors okay easy easy good there's no scope of changing sign have you given by any chance none of the above good good good turning pages and calculating and turning pages to cross reference achha monisha okay everyone i voted 56 good 32 people got it right guys look here the angle between the two vectors was the dot product minus 2 into 1 minus 2 3 into 2 plus 6 1 into minus 4 minus 4 the sum is coming out to be being an astronaut aya guys 0 sum is 0 at 90 degrees gi got it okay if there will be if i'll buy mistake beta will sense there is something fishy going on over there in the chat or in your class so could you explain i take an strict action okay please let's not so could you do once again yes please always see what we have to do the dot product i to i is minus 2 yes j to j is plus 6 and k to k is minus 4 isn't it 0 yes and dot product is equal to 0 i repeat if i'll buy mistake sense beta anything fishy going around in the chat or in the classroom okay i might change my tone of conversation okay good leaderboard so just because of one or two people don't do that so karun is the fastest one good good good good good very here we go to the next question so they are a vector f another vector that is perpendicular to f is schism my dear friend was 13th no problem no problem but okay please calculate look and respond for them to be perpendicular the dot product gotta be 0 calculate the dot product and put it equal to 0 there are two traps straightforward available for you okay so people messed up science 100 percent repeat people have messed up science people have messed up yeah i got it got it got it for that sake only they were there you know i got right i'm sure good good good good good relax relax let's see i even i'm curious to see this the old no no no no suits best over here right much along if this would have been plus then beautiful but it is not hence even okay sure i and j and only k straightforward answer how sir there is no i here zero there's no j here zero there's no k there zero oh god what is this sir i didn't get it sir i didn't get it okay so like if you have the time of the world the best way of solving this is like the time of the world do all the individual dot products oh so zero okay god four is six minus three nine is not equal to zero four into six is 24 no multiplication is not equal to zero seven into zero because there is no i here zero there's no j here zero there's no k there zero is equal to zero yes it is perpendicular if you fall down for this four trees are well three fours are 12 but minus minus plus is not equal to zero gi got it yes okay nine people only nine people got it no problem no problem no problem it's a learning right be careful next need a board now here we'll have a good beautiful shuffle current good good my dear friend raga good oh not like huge shuffle at the central table good good good good good good good sure good good good good good good thank you very much my dear friend thanks a lot thanks a lot like too many repetition like thanks a lot thanks a lot thank you very much but keep see all these are garnishing effects okay the core content the base of the cake should be learning good good good guys okay here we go to the next scenario that is the final question final shuffle at the leader board so it was easy may god bless us all let's go for it ready r for ready in the chat box no sparkling only single hours good good good good good good good here we go to the next and final question consider two vectors f1 and f2 the magnitude of the scalar product of these vectors is yeah raga you got it very good i was waiting for this kind of word in the chapter good good good good good nitya what happened today good good good good good good number are very good good good shivam no problem no problem meanwhile the question is on your screen you can see it and think about it 10 more seconds to go for it oops nitya sorry sorry no need to like spam it i got the news be safe please be safe please be safe please be safe look here so very confused yes relax a bit of the trap was two i you will jump and do will do six yes or no you will jump and you will do 20 you will mark delta i don't want you to do that so really good trap i is not here oh gone for the toss j is not here oh gone for the toss k is only here five four that 20 the magnitude is 20 g i got it good excellent excellent excellent excellent monisha you want a repetition today so one more time i'll do that see we are doing the dot product so i will write them two i plus five k actually i should write it as two i plus zero j plus five k and similarly i should write this as zero i plus three j plus four k dot product zero zero 20 monisha got it everyone my dear friends got it gi got it let's look at the leaderboard the beauty of the scene is that we are exactly finishing on time and here we go on winning the show very good karun very good very good clap for this beautiful person good good good good very good very good now clap to like clap for really everyone this time i felt it really good while conducting the quiz really really good very nice participation from everyone very good like good good good with a lot of love for you i am today feeling a lot of respect for you good guys really good sport very good very good very good thanks a lot guys good night bye bye thank you sir thank you sir good night and if you are safe and don't go out bye bye bye thank you sir bye dear thank you sir bye