I've been having difficulty with this problem for a while now. I'm given the following:
- Scalar product of vectors A & B = -3
- Magnitude of Vector product of A & B = 3
I'm now asked to find the angle between the two vectors
Notice that I don't have the components of each vector. All help is appreciated.
If the lengths of your two vectors are $x$ and $y$ and the angle between them is $\theta$, then you're given the scalar product, which is $xy\cos\theta$, and the magnitude of the vector product, which is $xy|\sin\theta|$. Adding the squares of these and remembering that $\cos^2\theta+\sin^2\theta=1$, you obtain $(xy)^2$. So you can find $xy$ and thence $\cos\theta$.