Math, asked by malliprasannakumar, 9 months ago

Q. 7 At what angle the vector (A+B) and (A-B) must act, so that the resultant is A+B?

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Answered by brainlyaryan12

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→ Q. 7 At what angle the vector (A+B) and (A-B) must act, so that the resultant is A+B?

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⇒ $\tiny{(A+B)^2=(A+B)^2+(A-B)^2+2(A+B)(A-B)Cos \theta}$

$\tiny{⇒{\cancel{A^2+B^2+2AB}}={\cancel{A^2+B^2+2AB}}+(A-B)^2+2(A+B)(A-B)Cos\theta}$

⇒ $0=(A-B)^2+2(A+B)(A-B)Cos\theta$

⇒ $-(A-B)^2=2(A+B)(A-B)Cos\theta$

⇒ $-\frac{(A+B)^{\cancel{2}}}{2{\cancel{(A+B)}}(A-B)}=Cos\theta$

⇒ $\large{\pink{\overbrace{\underbrace{\red{\theta=Cos^{-1}\bigg[\frac{(A+B)}{2(A-B)}\bigg]}}}}}$

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