Find the angle between lines AB and CD if A (6; -2; 6), B (6; -4; 4), C (4; 4; 6), D (2; 4; 4)

Let’s define the coordinates of the vectors:
AB = (6-6; -4 + 2; 4-6) = (0; -2; -2)
CD = (2-4; 4-4; 4-6) = (-2; 0; -2)
Vector lengths:
| AB | = √ (0 + (-2) * (- 2) + (-2) * (- 2)) = √4 + 4 = √8 = 2√2
| CD | = √ ((- 2) * (- 2) + 0 + (-2) * (- 2)) = √4 + 4 = √8 = 2√2
Scalar product:
AB * CD = 0 * (- 2) + (-2) * 0 + (-2) * (- 2) = 0 + 0 + 4 = 4
To determine the cosine of an angle, divide the dot product by the product of the lengths:
cos α = 4 / (2√2 * 2√2) = 4/8 = 1/2;
According to the table of cosines, we determine that the angle is 60 degrees.