Two vectors `vec A_(1) and vec A_(2)` each of magnitude A are inclinded to each other such that their resultant is equal to `sqrt(3) A.` What is the magnitude of the resultant of `vec A_(1) and -vec A_(2)` is

Options

A. `2A`
B. `sqrt3A`
C. `sqrt2A`
D. A

Answer

D

Explanation

Let ` theta` be the angle between ` A_(1) and A_(2)`
`:.` Resultant of `vec A_1 and vecA_2` is
`R^(2) =A_(1)^(2) +A_(2)^(2)+2A_1A_2cos theta`
or `3A^2=A^2+A^2+2"AA"cos theta`
or `cos theta =1/2 = cos 60^(@) " or " theta = 60^@`
The angle between `vecA_1 and - vecA_2` is `(180^(@) -60^(@))=120^(@) `
`:.` Resultant of `vecA_1 and - vecA_2` is
`R.=[A_1^2+A_2^2+2A_1A_2cos (180^@ -60^@)]^(1//2)`
`= [A^(2)+A^(2) +2 "AA" cos 120^(@) ]^(1//2)=A`