Angle between two lines

Find the angle between lines r (through P(5, 14, 11), direction (5, 4, 5)) and s (through Q(5, 14, 11), direction (3, 3, 7)).

Step-by-step solution

If the lines meet, the angle is measured in the plane containing them. If they are skew, move a parallel to one through a common point.
Rotate the plane that contains them flat to see the angle in true size.
Measure the angle between the two directions; if obtuse, take its supplement (the acute angle).
Check the order of magnitude: between 0° (parallel) and 90° (perpendicular).

Result: 21.19°.

The angle between two lines is always the acute one (0-90°): if the dot product is negative, use the absolute value.