Dot product calculator calculates the dot product of two vectors a and b in Euclidean space. Enter i, j, and k for both vectors to get scalar number.
a . b
Vector dot product calculator shows step by step scalar multiplication.
What is dot product?
Dot product is an algebraic operation that takes two equal-length sequences of numbers usually coordinate vectors, and returns a single number.
Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.
a . b usually read as a dot b.
Image credit: “Dot Product” by Math is Fun.
Dot product formula
Use this equation to calculate dot product of two vectors.
a × b = |a| |b| cos(θ)
|a| is length of vector a
|b| is length of vector b
θ is the angle between a and b
We can also find dot product by using the points of both vectors.
(ai aj ak) . (bi bj bk) = (ai . bi + aj . bj + ak . bk)
i, j, and k refers to x, y, and z coordinates on Cartesian plane.
Dot Product Formula from tutorial.math.lamar.edu.