# Determining coordinates of a point on a line perpendicular to a vector

## Homework Statement

The two lines L1: r = (-1,1,0)+ s(2,1,-1) and L2: r = (2,1,2) + t(2,1,-1) are parallel but do not coincide. The point A(5,4,-3) is on L1. Determine the coordinates of a point B on L2 such that vector AB is perpendicular to L2.

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## The Attempt at a Solution

I'm not sure where to start on this one. I know that eventually AB dot (2,1,-1) will equal 0, but I'm not really sure what to do with this question.

Homework Helper
Welcome to PF!

Hi adrimare! Welcome to PF! … I know that eventually AB dot (2,1,-1) will equal 0 …

That's right! So just write B in terms of t, and chug away. How do you do that? That's my main source of confusion here. How to write B in terms of t?

Mentor
Every point on L2 has to satisfy L2's equation, which means that every point on L2 has coordinates of (2 + 2t, 1 + t, 2 -t) for some value of t.

So I do (5,4,-3)-(2+2t,2+t,2-t) to get AB and then do AB dot (2,1,-1) and find t somehow?

Mentor
Almost. AB = <2 + 2t, 1 + t, 2 - t> - <5, 4, -3>. The dot product of AB and <2, 1, -1> should be 0.