# Line and unit sphere

1. Sep 18, 2015

### goonking

1. The problem statement, all variables and given/known data
Does the line through the points (−1, −1, −2) and (1, 2, 1) intersect the unit sphere? If so, find the point(s) of intersection.

2. Relevant equations

3. The attempt at a solution
do i also use r = r0 + vt but instead , use equation of sphere this time?

so it would be:

v=<2,3,3>

then using (-1,-1,-2) as the point

x = -1 + 2t y = -1 + 3t z=-2 + 3t

plugging these into x2 + y2 + z2 = 1

then solve for t

but then the math gets way too long and just doesn't seem to be the correct approach.

Last edited by a moderator: Sep 18, 2015
2. Sep 18, 2015

### vela

Staff Emeritus
You could try finding how close the line gets to the origin. If it's less than 1, it must intersect the unit sphere.

3. Sep 18, 2015

### goonking

do I need to use scalar projection for this?

4. Sep 18, 2015

### davidmoore63@y

What's wrong with your approach? I used it and got the answer quickly.

5. Sep 18, 2015

### Ray Vickson

The math does not get way too long; it is a bit messy, but sometimes that is how things are.

6. Sep 18, 2015

### goonking

whoops, there seems to be an error from the copy paste, it should be x2 + y2 + z2 = 1 and not x2 + y2 + z2 = 1. I will fix it right now.

hmmm, I cannot seem to edit my OP.

7. Sep 18, 2015

### Staff: Mentor

You can edit your post provided you do so within a short period of time. I have fixed your post for you.