Question

If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them, then $2\hat{u}\times 3\hat{v}$ is a unit vector for

• A. No value of $\theta$
• B. Exactly one value of a $\theta$
• C. Exactly two values of a $\theta$
• D. More than two values of $\theta$

Answer 1

Answer: (B)

Exactly one value of a $\theta$

Since given vector is unit vector
thus,
$|2\hat{u}\times 3\hat{v}|=1$

$\Rightarrow 6\left|\hat{u}\right|\left|\hat{v}\right|\left|\sin \theta \right|=1$
$\Rightarrow \sin \theta =\frac{1}{6}$
$2\hat{u}\times 3\hat{v}$ is a unit vector for exactly one value of $\theta$