- #1

fattycakez

- 21

- 0

## Homework Statement

"Let L1 be the line having parametric equations : x = 2 - s, y = -1 + 2s, z = 1+s and L2 be the line:

x = 1 +t, y = 2+ t, z =2t .

a. Do the lines intersect? If so, find the point of intersection.

b. Find the point P on the graph of L1 that is

*closest*to the graph of L2

**and**find the point Q on the graph of L2 that is

*closest*to the graph of L1.

*Hint*: Use the fact that the vector PQ will be orthogonal to the direction vectors of both lines. "

## Homework Equations

## The Attempt at a Solution

In part a, I set the parametric equations equal to each other and solved for t and s. It looks like the lines do not intersect.

I'm not sure how to go about part b. How does the hint that the vector PQ will be orthogonal to the direction vectors help me?

The direction vectors would be:

L1 = (-1, 2, 1) L2 = (1, 1, 2)

Any help is greatly appreciated!

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