How can I find the length of segment AB using the given line and planes?

[adrimare]

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.

Homework Equations

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?

 

[Mark44]

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.

Homework Equations

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?

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?

 

[adrimare]

How?

 

[Mark44]

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?

 

[adrimare]

That A has a y-value of 0 and B has an x-value of 0. Now what?

 

[Mark44]

Use your equation of the line. The two points have to be on the line, right? x= -8 + 2s, y= -6 + 2s, and z= -1 + s.