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If vecu and vecv are unit vectors and...

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

A

no value of ` theta`

B

exactly on value of `theta`

C

exactly two values of ` theta`

D

more than two values of ` theta`

Text Solution

Verified by Experts

The correct Answer is:
B
If is given that ` |vecu| = |vecv| =1 and theta` is the aucte angle between ` vecu and vecv` .
Now,
` 2 vecu xx 3 vecv ` will be a unit vector, if
` | 2 vecu xx 3 vecv| =1 `
` 6 | vecu xx vecv| =1 Rightarrow 6 sin theta =1 Rightarrow sin theta = 1/6`
As ` theta` is an acute angle, So, there is only one values of ` theta` for which ` 2 vecu xx 3 vecv` is a unit vector.
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