The resultant of A and B is `R_(1)` On reversing the vector B , the resulatnt `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))`

Answer

C

Explanation

(c) We have, `R_(1)^(2)=A^(2)=B^(2)+2ABcostheta`
and `R_(2)^(2)=A^(2)+B^(2)-2ABcostheta`
`:.R_(1)^(2)=R_(2)^(2)=2(A^(2)+B^(2))`