Scalar Product
An algebraic vector operation that multiplies two vectors to yield a scalar equal to the product of their magnitudes and the cosine of the angle between them.
Governing formula
A · B = |A||B| cos θ = Ax Bx + Ay By + Az Bz
SI unit
Various
In depth
The scalar product (dot product) measures directional alignment between vectors. It equals zero when vectors are orthogonal (θ = 90°).
Examples in the real world
Calculating mechanical work done by force along displacement (W = F · d).