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What does the determinant-like thing look like when you take the cross product of a vector by itself?


Rows two and three will be the same.

Two Rows Equal

Recall from the dark ages of high school math that if two rows of a determinant are the same, then it evaluates to zero. Each co-factor evaluates to zero, resulting in 0i + 0j + 0k  =  0.

The same will happen if one row is a multiple of another. These results reflect what we have already seen with geometrical vectors: ku × u   =   0.

The other properties of the cross product of geometrical vectors are also true of the cross product of their column matrix representations.


What were those properties again?