How to find the angle between two vectors?

Question

Here, I would like to describe my requirements .. Let's say we have two vectors named $\bf A$ and $\bf B$. Two vectors are in different magnitude and opposite directions and lay on different planes. These two vectors are parallel that is there is no point of intersection between these two. Now, how to find the angle between these two? I would be grateful to you if you could suggest me a better way to find the answer for the above. Thank you all.

Answer 1

Vectors aren't usually considered to have, uh, starting points, unless you're in a tangent space. Which unless you're doing something relatively advanced you aren't. You can use the dot product to find the angle between the directions of two vectors. $\vec u\cdot \vec v = \left|\vec u\right|\left|\vec v\right|\cos\theta = \sum_k u_k v_k$