One way to multiply two vectors is to take the dot product, which results in a scalar. Taking the dot product of two vectors, A and B, results in:

c = A • B = A B cos(θ)

where θ is the angle between A and B.

The dot product is ...

• zero when the vectors are perpendicular to one another
• maximum when they are parallel
• positive when the angle between the vectors is < 90
• negative when the angle between them is > 90

c = A • B = A_x B_x + A_y B_y + A_z B_z