The resultant of `vec(A)+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))`

Answer

C

Explanation

Given-
`vec(R)_(1) = vec(A) + vec(B) and vec(R)_(2) = vec(A) - vec(B)`
`R_(1)^(2) + R_(2)^(2) = A^(2) + B^(2) + 2AB cos theta+ A^(2) + B^(2) - 2AB cos theta`
`= 2(A^(2) + B^(2))`