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

3

Explanation

`R_(1)^(2) =A^(2) +B^(2) + 2AB cos theta `
`|vecR_2| = |vecA- vecB| rArr R_2^(2) = A^(2) + B^(2) - 2AB cos theta `
thus `R_1^(2) + R_2^(2) = 2(A^(2) + B^(2))`