Final answer:
To find the dot product of vectors A and B, multiply the corresponding components and add them together, resulting in A.B = -1. To find the angle between the vectors, use the formula that involves the dot product and the magnitudes of the vectors, applied by taking the inverse cosine.
Step-by-step explanation:
To find the dot product of the vectors A and B, we use the formula:
A.B = Ax Bx + Ay By + Az Bz
Assuming the second vector mentioned in the question is B = 2i + j - 2k, we can calculate the dot product as follows:
A.B = (3)(2) + (-1)(1) + (3)(-2) = 6 - 1 - 6 = -1
To find the angle between vectors A and B, we use the inverse cosine of the dot product divided by the product of the magnitudes of A and B:
cos(theta) = (A.B) / (|A| |B|)
We can calculate the magnitudes (|A| and |B|), then use them to find theta (the angle).
The provided equations are not directly relevant to the question, as they represent other vector operations.