Cross Product Calculator
Calculate the cross product of two vectors using the calculator below. See the steps to solve with the solution below.
Cross Product of Vectors (a × b):
Steps to Solve
Use the Cross Product Formula
(xa, ya, za) × (xb, yb, zb) = ({yazb - zayb}, -{xazb - zaxb}, {xayb - yaxb})
Substitute Values and Solve
Enter vectors a & b above to see the solution here
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How to Calculate the Cross Product of Two Vectors
A cross product is the product between two vectors, a and b, in a three-dimensional space. The resulting vector is perpendicular to both vectors a and b.
The cross product is denoted a × b, and it differs from the dot product in that the result will be a vector rather than a number.
Cross Product Formula
You can calculate the cross product of two vectors using the given formula:
a × b = |a|·|b|·sin(θ)·n
Where:
- |a| = magnitude of vector a
- |b| = magnitude of vector b
- θ = angle between the vectors
- n = unit vector perpendicular to the plane containing a and b
You can use our magnitude and angle between two vectors calculators to solve for |a|, |b|, and θ.
Practical Application
You can use an alternative formula to reduce the complexity of calculating the cross product in a three-dimensional space.
(xa, ya, za) × (xb, yb, zb) = ({yazb – zayb}, -{xazb – zaxb}, {xay2 – yaxb})
To use the formula, simply substitute the values of two vectors for xa, ya, za, xb, yb, & zb to solve the resulting vector.
To solve x, y, and z for vector c, follow these steps:
xc = {yazb – zayb}
yc = -{xazb – zaxb}
zc = {xay2 – yaxb}
You might also be interested in our vector addition and vector subtraction calculators.