Determine that a and b are parallel,

where a = 2i - 3j, and b = -4i + 6j.

If two vectors are orthogonal, the angle between them is 90° , making the cosine of the angle between them 0.

If two vectors are parallel, the angle between them is either 0° or 180° , making the cosine of the angle between them 1 or -1.

Hence, we proceed by finding the cosine of that angle:

. Here this becomes

The two vectors must have a 180° angle between them.