For b), first rewrite the line as .
The distance from the origin to the line is
The minimum distance will the value of for which the derivative is and where the second derivative is positive.
a) By looking at their intersection and their direction vectors, show that the following lines are skew:
(x,y,z) = (2, -1, 6) + t(1, 2, 0)
(x, y, z) = (1, 4, 4) + u(2, -3, 1).
b) Find the closest point to the origin on the line (x,y,z) = (2, -1, 6) + t(1, 2, 0) and the shortest distance from the origin to that line.