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.
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)
i, j, and k represents x, y, and z coordinates on Cartesian plane.
Formula of Cross Product. Retrieved from MathisFun.