The resultant of two vectors `vecP and vec Q` is `vec R`. IF the magnitude of `vec Q` is doubled, the new resultant becomes perpendicular to `vec P`. Then the magnitude of `vec R` is

Options

A. `P+Q`
B. Q
C. P
D. `(P+Q)/2`

Answer

B

Explanation

In first case
`R= sqrt(P^2+Q^2+2PQ cos theta)` ….(i)
where `theta` is the angle between P and Q.
In second case,
`(vecP +2 vecQ).vecP=0`
or `vecP. vecP +2 (vec Q. vecP)=0`
or `P^2+0=0`
or `P=0`
Putting P=0 in Eq. (i) we get
`R= sqrt(0+Q^2+0)=Q`