Linear Algebra
Intermediate

Dot Product

Scalar product of two vectors.

Formula

a⃗⋅b⃗=∑iaibi=∣a∣∣b∣cos⁡θ\vec{a}\cdot\vec{b} = \sum_i a_i b_i = |a||b|\cos\theta

Variables

\vec{a},\vec{b}Vectors
\thetaAngle between them

Example

(1,2,3)·(4,5,6) = 4 + 10 + 18 = 32.

Did You Know?

The dot product is zero exactly when two vectors are perpendicular — a quick orthogonality test.

vectordot product