# Homework Help: Find the distance from the origin to the line x=1+y, y=2-t, z=-1+2t

1. Sep 25, 2011

### goomer

Question: Find the distance from the origin to the line x=1+t, y=2-t, z=-1+2t

Equations: r = r0 +tv

Attempt:

I think I solved for the vector line equation correctly:

r = < 1, 2, -1> + t< 0, -1, 2>

But I don't know where to go from there. Help please!

Last edited: Sep 25, 2011
2. Sep 25, 2011

### flyingpig

3. Sep 25, 2011

### Dick

What kind of a approach is your book, notes or lectures using? You could differentiate |r|^2 with respect to t and find the minimum if you are doing calculus. Or you could do vector operations like dot and cross product to find it. You've got to have some clue.

4. Sep 25, 2011

### goomer

Well, we've learned that the distance between a point and a plane is

| ax0 + by0 + cz0 + d | / √ ( a^2 + b^2 + c^2)

but this is finding the distance between a point and a line, so I don't see how it would help, or if it's even relevant.

5. Sep 25, 2011

### flyingpig

What is the distance formula?

6. Sep 25, 2011

### Dick

No, probably not really relevant. Do you know the vector dot product? Stuff like that? If your line is L(t)=r0+tv, you want to find a point on your line where L(t)-<0,0,0> is orthogonal to the direction vector of your line, v. Do you see why?