Magnitude of Cross Product given 2 vector magnitudes and angle between them?

Question

if the magnitude of vector U is 6 and the magnitude of vector V is 9, and the angle between these vectors is 60 degrees, what is ||U x V||? Why is the answer not 54Sin(60)?

Answer 1

If you really meant $54\sin(60)$, then it is wrong because it should be $54\sin(60^{\rm o})$. Check whether your calculator is set to degrees or radians.

Answer 2

Yes it is correct since

$$|\vec u \times \vec v|=|\vec u||\vec v|\sin \theta$$

Note also that this value correspond to the area of the parallelogram spanned by the two vectors and thus the area of the triangle with sides $|\vec v|$ and $|\vec u|$ is given by

$$A=\frac12|\vec u||\vec v|\sin \theta$$