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If I have perpendicular vectors $ \vec{a}$ and $\vec{b} $, then $\vec{a}.\vec{b} = 0$. What happens if they are co-linear? Would you just get $\vec{a}.\vec{b} = ||\vec{a}||.||\vec{b}|| . 1 $?

Also, does $\vec{a}$ x $\vec{b} = 0$ if they're co-linear?

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up vote 1 down vote accepted

For colinear vectors you have $\vec a\cdot \vec b=\pm ||\vec a||\cdot|\vec b||$. And, yes, you also have $\vec a\times \vec b=\vec 0$ for colinear 3D vectors.

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