Dot Product Calculator
Solve dot product problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Reviewed by Manoj Kumar, Mathematics Educator
Formula
AยทB = aโbโ + aโbโ + aโbโ | Angle ฮธ = arccos(AยทB / (|A| ร |B|))
The dot product (scalar product) of two vectors equals the sum of products of corresponding components. It also equals |A||B|cos(ฮธ), where ฮธ is the angle between them. Dot product = 0 means vectors are perpendicular.
Worked Examples
Example 1: 3D vectors
Problem:A = (1,2,3), B = (4,5,6)
Solution:Dot = 1ร4 + 2ร5 + 3ร6 = 4 + 10 + 18 = 32. Angle โ 12.93ยฐ
Result:AยทB = 32, angle โ 12.93ยฐ
Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy