If $\vec u$ and $\vec v$ are unit vectors and θ is the acute angle between them, then $2\vec u×3\vec v$ is a unit vector for

exactly one value of θ

It is given that $|\vec u|=|\vec v|=1$ and θ is the acute angle between $\vec u$ and $\vec v$.

$∴ |\vec u×\vec v|= \sin θ$

Now,

$2\vec u× 3\vec v$ will be a unit vector, if

$|2\vec u× 3\vec v|=1$

$⇒6|\vec u×\vec v|=1⇒6\sin θ=1⇒\sin θ=\frac{1}{6}$

As θ is an acute angle. So, there is only one value of θ for which $2\vec u× 3\vec v$ is a unit vector.