- #1

Dr Zoidburg

- 39

- 0

## Homework Statement

following equations represent lines P nad Q in 3 dimensional space:

P: 2-x=y+1=(z-3)/2

Q: 5-x=y-2=(z+1)/2

(a) Show that P & Q are two different lines which are parallel

(b) Find the distance between the two lines, measured along a line perpendicular to P & Q.

## Homework Equations

## The Attempt at a Solution

(a) I attempted to turn the above equations into vector equations. I came out with the following:

v(P) = (2,-1,3) + t(-1,1,2)

v(Q) = (5,2,-1) + s(-1,1,2)

I concluded that since the the direction vectors are the same, therefore the lines are parallel.

correct?

(b) Not sure what to do here. Do I use the distance formula for between two points?

ie.

[tex]\sqrt{(2-5)^{2}+(-1-2)^{2}+(3--1)^{2}}[/tex]

I then get [tex]\sqrt{34}[/tex]

correct? (I have the nagging feeling it ain't!)

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