# Find length of segment AB

1. Apr 18, 2010

1. The problem statement:

The line r=(-8,-6,-1) + s(2,2,1) intersects the xz- and yz-coordinates planes at points A and B, respectively. Determine the length of line segment AB.

2. Relevant equations

3. The attempt at a solution

I know that for the line, x= -8 + 2s, y= -6 + 2s, and z= -1 + s. I think the normals to the xz- and yz- planes are (0,1,0) and (1,0,0) respectively. Do I just stick the parametric equations of the line into the Cartesian equation of each of the planes to get something or do I have to use different numbers?

2. Apr 18, 2010

### Staff: Mentor

Knowing the normals to the two coordinate planes isn't useful in this problem, but something that is useful is that every point on the x-z plane has a y coordinate of 0. There is a similar property for every point on the y-z plane. Can you use this information in your problem?

3. Apr 18, 2010

How?

4. Apr 18, 2010

### Staff: Mentor

You know that the line intersections points A and B, and that these points are on, respectively, the x-z and y-z coordinate planes. What do you know about point A? Point B?

5. Apr 19, 2010