Vectors Question 198

Question: The resultant of $ \vec{A} $ and $ \vec{B} $ is $ {{\vec{R}}_1} $ . On reversing the vector $ \vec{B}, $ the resultant becomes $ {{\vec{R}}_2} $ . What is the value of $ R_1^{2},+,R_2^{2},? $

Options:

A) $ A^{2}+,B^{2} $

B) $ A^{2}-B^{2} $

C) $ 2(A^{2}+,B^{2}) $

D) $ 2(A^{2}-,B^{2}) $

Show Answer

Answer:

Correct Answer: C

Solution:

[c] $ R_1^{2},=,A^{2}+,B^{2}+,2,AB,\cos \theta $

$ R_2^{2},=,A^{2}+,B^{2}-,2,AB,\cos \theta $
$ \

Therefore $ $ R_1^{2},+,R_2^{2},=2,(A^{2}+B^{2}) $