If ` vecu and vecv ` are unit vectors and `theta` is the acute angle between them, then ` 2 uvecu xx 3vecv` is a unit vector for

Options

A. exactly two value of `theta`
B. more than two values of `theta`
C. no value of `theta`
D. exactly one value of `theta`

Answer

D

Explanation

Since, `( 2hatu xx 3 hatv) ` is a unit vector.
`rArr |2 hatu xx 3 hatv|= 1 rArr 6|hat u| |hatv||sin theta|=1 `
`rArr sin theta = (1)/(6) " " [ because |hatu | = | hatv|=1] `
Since `theta` ios an acute angle, so there is exactly one value of `theta` for which `(2 hatu xx 3hatv)` is unit vector .