# Angle Between Two Vectors

The angle between two vectors and is given by the formula:

#### Examples

Calculate the dot product and the angle formed by the following vectors:

1. = (3, 4) and = (−8, 6)

· = 3 · (−8) + 4 · 6 = 0

2. = (5, 6) and = (−1, 4)

· = 5 · (−1) + 6 · 4 = 19

3. = (3, 5) and = (−1, 6)

· = 3 · (−1) + 5 · 6 = 27

Given the vectors = (2, k) and = (3, −2), calculate the value of k so that the vectors and are:

1 Perpendicular.

2 Parallel.

3 Make an angle of 60°.

Find the value of k if the angle between = (3, k) and = (2, −1) is:

1 **90°**

2 **0°**

3 **45°**

Calculate the angles of the triangle with vertices: A = (6,0), B = (3,5) and C = (−1,−1).