 इं औरका आखमी च्यन एक आछते नागस प्रत्र हैं। दोँस तो आज हम च्रचा खा ہےंगे इंक बहुत फीट लाग झा चा आचढी स्झी अशी आचा जाचा बहुत ऎज दे पुर्छिल राशा प्रत्र ते कों नायathon is a very special by physics law that is known as triangle law of vector addition. अपको मालु में एक वेक्तर क्या होता है और वेक्तर का प्रेोग हम कैसे फिजिकस के विबहन छेट्रो में करते हैं तो उसका वहाती आप पन्टमेंटल प्रेषिपल है अब अपरेक्तर का जिसका नाम है त्रींगल लोग अप वेक्तर अदीशन वो आज हम इस जीोजिप्रा जोमेट्री तूल के जर ये दरशाने की कोछिच कर रहें नाही केवल ये हम मैठमाटेक्स के आँगल से, बट अगर अप में यस में तूर्ज दि एँडिन्ड दिखाएम आप को कैसे इसी माद्ट्यम से आप आप आरट भी कर सकते हैं तो लिए जिन्ट येद फैस्टनेटीं देद बादने बादने जामने अगर थे हैं? आपको मालुब होगा के जिन्ट भी ग्राफ्रिक सुफ्फर होगा आपको मालुब होगा फोटोश्प या कोरुल ड्रो पहले हूँँ अगर ता ता अभी भी है और जितने भी अदर ग्राफ्रिक सुफ्फर होते है, मूल तह जो है मैठमाटिक सी बाग्राउन में होगा है कुकी सारे कोडनेट जोमेट्री या वेक्टर आलजिब्रा केले या काल्पुलस केले सारे इनहीं आमो के प्रियोग से ही हम उन सुफ्फर्फर्ष की रचना करते हैं तो मैठमाटिकस और इनवे आर्ट is very deeply linked सो उसकी भी चर्चा हम करेंगे तो पहले जान लेते हैं कि ये वेक्टर ट्राइंगल लोग वेक्टर एडिशन है क्या तो जैसर के आपको आपको अपनी स्क्रीन पे दिख्रा होगा आबी एक वेक्टर है और बी सी तुसरा वेक्टर है जो 44 दिगरी के अंगल पे आबी से इंख्लाईंगल है तो जो इसका resultant होगा that is the sum of a, b and bc आवे हमें पता है is given by a, c अगर आबी एक वेक्टर बी सी तुसरा वेक्टर अगर एक त्रंगल के 2 पाट्स को तुसरा वेक्टर है जो तो इन दोनो का resultant या sum जो होगा वो रिप्रज़न्त होगा त्रंगल के 3 रे साएट से आबी, b, c are the two vectors whose sum or resultant is given by a, c आबी, b, c are the two vectors whose sum or resultant is the value of alpha in this case is 4 degrees and value of 5 which I have calculated geometrically it is 16.74 in this particular configuration understood so what is it once again a, b plus b, c these are 2 vectors the length of a, b the magnitude of the vector being represented the geometric length of the b, c the magnitude of the vector being represented रेट्र से यूँ आप देअगा जोद बिजके अब वेक्तर से नहींने सोगी रेट्र बिजके शुएगा और तो शो वेक्तर शुएगे यूँ बिजके आप यहने सोगी खादा है. जो फम्ट्ट्ट्ट्ट्ट्ट्टा, ईबि उसके बीज का है तो आपको पदः है खिजी वेक्तर को रिप्रज्टाड करने के लिए हमें 2 कंबाउतिस की जोडफ लब लबई है बएद्र लिए थी तो रब वेक्तार् से म Nh Firstly 1, magnitude is the motor's direction. तो आपनोग, आपनोग, आपनोग, आपनोग आपनो आसम्सदेino Let's magnitude is the motor's length. और नहां, यह सबवोग यह साथ. यह यह साथ आपनोग, अप्का।, 갑자기 the direction is from that angle. तो हैंस ये होगाया आप का ध्यामगल लोग अख्वेक्तर एदीशन ये से ब ब यही रहाँ भगे बी आब नहीं थे वेक्तर था किदी सैथ तो बगे बगे भगे बगे बगे बगे, दे आदा थे तरीज सैद ये इसो उगाए नहीं चाह खाल हैं. इसली ? खेल्डिदूरूप पब वीॐ अगी मखिल्दिडीरण च़ाको। च्छग। आप फुल्त यह असी वी-सी-गे नाप मुझाड़़ी आप पै़दा गरूषत् तरंगल लगाना उआप पै़दा गरूप उस्फॉल्ला यह नहां मुस्दर् to mod of ac that is the magnitude of vector ac is under root mod of ab square that is is ab ka length ka square plus is bck length ka square plus twice of ab and bck length into the cost of angle between ab and bc which is 44 degrees given by alpha or theta whichever way you can say it alpha is theta in this case so you can you can get what is the magnitude of ac. secondly the phi the angle between the resultant and the first vector is phi you can clearly see tan phi is c e upon a e so i am not shown those calculations i have not shown those calculations but this is not a big thing and you will get this value of phi in this case 16.74 so what happens if i change this point c. so now i am changing it and depending upon a and b and angle you can have different different locations and positions for the vectors and you can see how the resultant of the vector is dependent on these three factors. you can see if i move a then how the value of ac and phi is changing on the screen you can see if i change b then you can see the value of ac and phi is changing and same way if i change theta then it changes. now the fun fact is that now we will make some design from it. so that is the most important thing and another most important thing which you are going to discuss here. so let's see how this design will turn out and what is in this design. so let's see what i am doing that i am animating it by turning on this trace. so let's see what it is so this is making a new design here and as the value of a and b and c is changing you can see a new pattern emerge. so this is interesting. this is quite interesting and you will see a new pattern on your screen. what is that? that is the trace of point c. so one thing you will be seeing in this is that it is coming up with a symmetrical design. so hence if i change it then it will oscillate in repeat mode and you will be able to see deeper details of this design. so you can see how by changing a, b and theta we can get a very different type of use of vector algebra. isn't it? so we are also able to make a design here. so this is one pattern. if you see i will stop it now and try a new one again. and let's change the values of a and b all together and i will get some variation in size so that everything is in this screen. so let's see how this design will turn out in this case. this can also be a bad answer. so let's see if you see again you will see symmetry again. why? because this is an oscillatory system. this will continue to change. so here see a new design is coming up. interesting thing will be that on the left side of the screen what kind of design it will be. this will be interesting. and you see again in this case also a very symmetric figure is coming up. so let's take one more attempt and give it a little more variation and see what this design will turn out. so let's see this and again so i have again brought a little variation in these three parameters. and again it will turn out to be a different design. interesting thing will be to see if it can give a recognizable shape. so if you see again a symmetric figure is coming up. then you will know when it is complete. yeah so if you see now it's again very very symmetrical. again a symmetrical figure or two leaves is coming up. right? a design is coming up. so i hope you have understood that because of mathematics we can also work in the field of design. so all the design software that are utilized for different designing and for that matter even for gaming whatever you know you must have heard the name of the software like unity or blender whatever these all work on the basis of graphics and the basic work behind the graphics is of mathematics. so friends if you want to make your career in this field then it will not be without mathematics. so this is a good thing that if you are interested in mathematics and it will be very easy for you. so i hope you liked this explanation. and also that how to be designed with the help of vectors on your screen. it can be if you are interested in this then you can also do these different simulations on your screen. it's free software. learn from it and see how mathematics can be made interesting. so thanks for watching this and we'll come back again with another explanation another simulation and let's see if we have some relationship though we believe or i believe that there is but for you also to believe we have to come with more explanation as into how mathematics is very closely linked to our day-to-day life. thanks for watching see you and bye-bye