Resultant of two vectors `vecA and vecB` is of magnitude P, If `vecB` is reversed, then resultant is of magnitude Q. What is the value of `P^(2) + Q^(2)` ?

Options

A. `2(A^2 + B^2)`
B. `2(A^2 + B^2)`
C. `A^2 - B^2`
D. `A^2 + B^2`

Answer

A

Explanation

Let `theta` be angle between `vecA and vecB`
`:.` Resultant of `vecA and vecB` is `p = sqrt(A^2 + B^2 + 2 AB cos theta)" "……(i)`
When is reversed, then the angle between `vecA and vecB` is `(180^@ - theta)`.
`:.` Resultant of `vecA and vecB` is `Q = sqrt(A^2 + B^2 + 2AB cos (180^@ - theta))`
`Q = sqrt(A^2 _ B^2 + 2 AB cos theta)`
Squaring and adding (i) and (ii), we get `P^2 + Q^2 = 2(A^2 + B^2)`.