I'm trying to find the perpendicular distance distance between a line given by a directional vector traveling from the origin to some point A and point B in 3D space. I dotted the vector OA and OB and found the angle between them using the dot product of the vectors. Can I use sine theta multiplied by magnitude of OB to find the perpendicular distance? Can I find the directional vector of the perpendicular by multiplying OB by sin theta? If not could you explain why?
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Vector $OB$ is in the direction of $OB$? If you multiply it by a scalar such as $\sin\theta$ its direction will still be parallel to $OB$. Not perpendicular. Look up rejection of $OB$ from $OA$ to see how to do it.
