For two vectors:

• a = (ax)i + (ay)j + (az)k

• b = (bx)i + (by)j + (bz)k

a + b = (ax + bx)i + (ay + by)j + (az + bz)k

The cross product of two vectors is the product of their magnitude and sine of the angle between them.

For equal vectors the angle between them is 0 and sin 0 = 0

This makes the cross product of equal vector equal to the zero vector

If two vectors have a cross product equal to zero, they are equal vectors.