Magnitude of Cross Product given 2 vector magnitudes and angle between them?
By Emma Terry •
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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)?
2 Answers
$\begingroup$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.
$\endgroup$ $\begingroup$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
$$A=\frac12|\vec u||\vec v|\sin \theta$$
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