Dot Product Calculator

Cross product calculator calculates the cross product of two vectors a and b in three-dimensional space. Enter i, j, and k for both vectors to get the resultant vector c.

c = a × b

This vector cross product calculator shows step by steps vector multiplication.

What is cross product?

Cross product is a multiplication of two vectors in three-dimensional space. It is denoted by the symbol ‘×’.  Cross product of two vectors a and b is a vector that is perpendicular to both a and b.

Note: Read a × b as a cross b.

cross product

Image credit: “Cross Products” by Khan Academy.

Cross product formula

Below equation is used to find the cross product of two vectors.

a × b = |a| |b| sin(θ) n

In this equation:

|a| is length of vector a

|b| is length of vector b

θ is the angle between a and b

n is the unit vector perpendicular to a and b.


We can also calculate cross product by using the coordinate points of both vectors.

(ai aj ak) × (bi bj bk) = (aj × bk - ak × bj    ak × bi - ai × bk    ai  bj - aj × bi)

Where

 i, j, and k represents x, y, and z coordinates on Cartesian plane.

 

References:

Formula of Cross Product. Retrieved from MathisFun.