Dot Product Calculator
Compute the dot product (scalar product) of two vectors, find the angle between them, and determine whether they are orthogonal. Enter the components of each vector and get instant results.
The dot product is one of the most important operations in vector algebra. For two vectors A = (a1, a2, a3) and B = (b1, b2, b3), the dot product is A · B = a1b1 + a2b2 + a3*b3. The result is a scalar, not a vector.
Geometrically, the dot product relates to the angle between the vectors: A · B = |A| |B| cos(theta). This means you can find the angle using theta = arccos(A · B / (|A| |B|)). When two vectors are perpendicular (orthogonal), their dot product is zero because cos(90°) = 0.
The dot product has many applications: computing projections, testing perpendicularity, calculating work done by a force along a displacement, determining lighting in computer graphics (Lambert's cosine law), and finding the component of one vector along another direction.