Cross Product

The cross product of two 3D vectors creates a vector that is perpendicular to the plane where the two vectors lie. A normal is a vector that is perpendicular to a surface, such as a plane. The cross product lets you calculate normal vectors. Use the following formula to calculate the cross product:

v1 = < x1, y1, z1 >  v2 = < x2, y2, z2 >
v1 X v2 = < x3, y3, z3 >
x3 = (y1 * z2) – (z1 * y2)
y3 = (z1 * x2) – (x1 * z2)
z3 = (x1 *y2) – (y1 * x2)

As you can see from its formula, the cross product is more complicated to calculate than the other operations covered in this article. Let’s look at an example.

v1 = < -5, 3, 6 >  v2 = < 4, 5, 7 >
x3 = (3 * 7) – (6 * 5) = 21 – 30 = -9
y3 = (6 * 4) – (-5 * 7) = 24 – (-35) = 59
z3 = (-5 * 5) – (3 * 4) = -25 – 12 = -37
v1 X v2 = < -9, 59, -37 >

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