1.

If hatu and hatv are unit vectors and theta is the acute angle between them, then 2hatuxx3hatv is a unit vector for

Answer»

exactly TWO value of `THETA`
more than two values of `theta`
no value of `theta`
exactly one value of `theta`

Solution :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 .


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