If u and v are unit vectors and is the acute angle between them, then 2 u3 v is a unit vec…

Question

If $\hat u$ and $\hat v$ are unit vectors and $	heta$ is the acute angle between them, then $2\hat u	imes3\hat v$ is a unit vector for:

Accepted Answer

$|2\hat u	imes3\hat v|=6|\hat u||\hat v|\sin	heta=6\sin	heta$. Setting this equal to $1$: $\sin	heta=\dfrac16$, which has exactly one solution for acute $	heta$.

Solutions · 1