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. `sqrt(3)A`
C. `sqrt(2)A`
D. A

Answer

D

Explanation

Given : `|A_(1)|= |A_(2)| =A`
`therefore sqrt (3) A = sqrt (A^(2) + A^(2) +2A cdot A cos theta)`
`therefore 3A^(2) = 2A^(2) +2A^(2) cos theta`
`therefore A^(2) = 2A^(2) cos theta" "therefore cos theta =(1)/(2)" "therefore theta =60^(@)`
When `A_(2)` is reversed, the angle between them becomes `120^(@)`.
`therefore R = sqrt (A^(2) + A^(2) + 2A cdot A cos (120^(@)))`
`[because cos 120^(@) =-(1)/(2)]`
`therefore R = sqrt (2A^(2) + 2A^(2) xx(-(1)/(2)))`
`therefore R = sqrt (A^(2)) =A`