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

`R_(1)^(2)=A^(2)+B^(2)+2AB cos theta`
`|vecR_(2)|=|vecA-vecB|rArrR_(2)^(2)=A^(2)+B^(2)-2AB cos theta`
thus `R_(1)^(2)+R_(2)^(2)=2(A^(2)+B^(2))`