Verify (a + b) x (a + b) = 0.  What can be said about two vectors whose cross product is zero?

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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.

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