Calculus III - Equations of Lines

Show General Notice Show Mobile Notice Show All Notes Hide All Notes

General Notice

I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.

Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.

Paul
February 18, 2026

Mobile Notice

You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 12.2 : Equations of Lines

Back to Problem List

7. Does the line given by \(x = 9 + 21t\), \(y = - 7\), \(z = 12 - 11t\) intersect the \(xz\)-plane? If so, give the point.

Show All Steps Hide All Steps

Start Solution

If the line intersects the \(xz\)-plane there will be a point on the line that is also in the \(xz\)‑plane. Recall as well that any point in the \(xz\)-plane will have a \(y\) coordinate of \(y = 0\).

Show Step 2

So, to determine if the line intersects the \(xz\)-plane all we need to do is set the equation for the \(y\) coordinate equal to zero and solve it for \(t\), if that’s possible.

However, in this case we can see that is clearly not possible since the \(y\) equation is simply \(y = - 7\) and this can clearly never be zero.

Show Step 3

Therefore, the line does not intersect the \(xz\)-plane.