One way to multiply two vectors is to take the dot product, which results in a scalar. Dot products are important in a case such as work, when the work done by a force in moving an object depends on the component of the force in the direction of the displacement.

W = F · d = F d cos(θ)

Note that 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