Question

Using the definition of the scalar product, find the angle between A = i − 2j + 2k and B = 3j + 4k. Explanation please, not just the answer.

Answer 1

Let U and V be vectors. A fundamental property of the scalar product is that

U.V = |U| |V| cos(theta)

where theta is the angle between U and V, and |U| and |V| are the magnitude of the vectors respectively.

Now, using this relation, it should be easy to find the angle between any two (non-zero!) vectors.

Answer 2

How do I evaluate the left side though?

Answer 3

In general, for two vectors, U = (u1, u2, u3), V = (v1, v2, v3), what is the definition of
U.V ?

Answer 4

You're quiet, so I'm guessing you don't know. The definition of the dot product between two vectors, U and V is

U.V = u1 v1 + u2 v2 + u3 v3

Answer 5

Oh okay yeah. :) Thanks!