# Find vector orthogonal to two lines

## Homework Statement

L1 pass through the points (-2,36,9) and (-8,44,12)
L2 pass through the points (55,-31,7) and (41,-16,13)
Find a point P on L1 and a point Q on L2 so that the vector $$\vec{}PQ$$ is orthgonal to both lines.

## Homework Equations

Dot product/ Cross product

## The Attempt at a Solution

Equation for L1: x(t) = -2 -6t; y(t) = 36+8t; z(t) = 9 + 3t
Equation for L2: x(s) = 55 -14s; y(s) = -31 +15s; z(s) = 7 +6s
I stuck from here. I can find the intersect pt if the 2 lines are intersect, but this look intersect but have a space between them.

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