If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them, then $2 \hat{u}…
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
exactly two values of $\theta$
more than two values of $\theta$
no value of $\theta$
exactly one value of $\theta$
Solution
$|2 \hat{u} \times 3 \hat{v}|=1$
$\begin{aligned}
& 6|\hat{u}\|\hat{v} \| \sin \theta|=1 \\
& \sin \theta=\frac{1}{6}
\end{aligned}$
Hence there is exactly one value of $\theta$ for which $2 \hat{u} \times 3 \hat{v}$ is a unit vector.