Determine that a and b are neither orthogonal nor parallel,

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

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

Since this is positive and neither 0 nor 1, the two vectors must have an acute angle between them.