# Help with Problem

• Dec 5th 2005, 11:21 PM
fiveluck
Help with Problem
Q: Find a line perpendicular and intersecting the lines: (t, 1-t, 2t) and (2t, t, t).

What I am thinking so far:
Treat the second line like (2s, s, s)

Normal Vector: Cross Product of the two: (t-3t^2, 3t^2, 3t^2 - 2t)

Find 2 equations using cross product then solve for s and t.

Need help :) Thanks!
• Dec 6th 2005, 04:46 AM
CaptainBlack
Quote:

Originally Posted by fiveluck
Q: Find a line perpendicular and intersecting the lines: (t, 1-t, 2t) and (2t, t, t).

What I am thinking so far:
Treat the second line like (2s, s, s)

Normal Vector: Cross Product of the two: (t-3t^2, 3t^2, 3t^2 - 2t)

Find 2 equations using cross product then solve for s and t.

Need help :) Thanks!

Let the points on the perpendicular at which it intersects the two
lines be u and v. Then u and v are the points for which the distance
between points on the two lines is minimised.

So express the distance between a pair of points, one on one line
and the other on the second line, in terms of t and s, then find
the values of t and s which minimise the distance between the
two points. This will alow you to find the required points, then
you need only find the line through these two points to answer the
question.

RonL