To determine the angle between two vectors $\mathbf{A}$ and $\mathbf{B}$, we use the following formula from vector algebra:

$\cos \theta = \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|}$

Where:

• $\theta$ is the angle between the two vectors.
• $\mathbf{A} \cdot \mathbf{B}$ is the dot product of the vectors.
• $|\mathbf{A}|$ and $|\mathbf{B}|$ are the magnitudes (or lengths) of vectors $\mathbf{A}$ and $\mathbf{B}$, respectively.

To calculate the angle $\theta$, rearrange the equation:

$\theta = \cos^{-1} \left( \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|} \right)$

If you provide the components of vectors $\mathbf{A}$ and $\mathbf{B}$, I can calculate the dot product and magnitudes, then find the angle between them.

Would you like to try an example or have further clarification?

Here are some related questions:

1. How is the dot product of two vectors calculated?
2. What is the physical interpretation of the angle between two vectors?
3. How can I compute the magnitude of a vector in 2D and 3D?
4. What is the difference between the dot product and the cross product?
5. How does the angle between two vectors affect their relationship (parallel, perpendicular, etc.)?

Tip: If the dot product of two vectors is zero, the vectors are perpendicular (the angle between them is $90^\circ$).