Dot Product Calculator
Find the dot product of two vectors, in 2D or 3D, with the step-by-step working shown in clean math notation.
What is the dot product?
The dot product (also called the scalar product) of two vectors returns a single number. There are two equivalent formulas: the component form $vec{a} cdot vec{b} = a_1 b_1 + a_2 b_2 + a_3 b_3$ and the geometric form $vec{a} cdot vec{b} = |vec{a}||vec{b}| cos theta$.
Worked examples
2D: $(3, 4) cdot (5, 6) = 15 + 24 = 39$. 3D: $(1, 2, 3) cdot (4, 5, 6) = 4 + 10 + 18 = 32$.