Perpendiculars to two vectors So this is more than likely a simple question that has been asked before, but if have 2 lines described by the formula:
$V = (x,y,z) + L (i,j,k)$
i.e.  a line described by a position and a length along a unit vector
How would I find the line that is perpendicular to both lines?

Consider the vector from a point of the first line to a point of the second line and express that it is orthogonal to the direction of both lines.
$$(P_1+\lambda_1D_1-P_0-\lambda_0D_0)\cdot D_0=0\\(P_1+\lambda_1D_1-P_0-\lambda_0D_0)\cdot D_1=0,$$
or
$$\lambda_1D_1\cdot D_0-\lambda_0D_0^2=(P_0-P_1)\cdot D_0\\\lambda_1D_1^2-\lambda_0D_0\cdot D_1=(P_0-P_1)\cdot D_1$$
Solve the $2\times2$ linear system and you get two points on the desired line.
