How do I find the sine of the angle between two vectors?

I'm assuming you either have the components of the vectors, or their magnitude and angle. You will need to apply the cross product to get the sine.

Honestly, it'd be much easier if someone explains it to you on paper, it's too long to type here and may seem hard, but it's pretty easy.

Let's assume the vectors are U and V.

U X V (cross product) = |U| * |V| * Sin(theta)

Which is the magnitude of the first vector, multiplied by the magnitude of the second vector, multiplied by the sine of the angle between them.

Now, you have the magnitude of both vectors, but lack the sine and the actual cross product.

To get the cross product, apply this:

Replace a with U and b with V.

Doing this will get you the components, you want the magnitude, I assume you know it, but anyway, the magnitude is ##sqrt(x i^2 +yj 2 + zk ^2)## It's the square root of all the components squared.

Replace in the original law, and solve for sine.