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 the angle between
`vecA and vecB`
`:.` Resultant of `vecA and vecB `
`P = sqrt(A^(2)+B^(2)+2AB cos theta)" "...(ii)`
When `vecB` 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^2-2AB cos theta)" "...(ii) `
Squaring and adding (i) and (ii) , we get
`P^(2) + Q^(2) = 2 (A^(2) +B^(2))`