Video Transcript
Given that the point π₯, π¦, π§ lies in the π₯π¦-plane, determine its π§-coordinate.
In this question, weβre given a three-dimensional point π₯, π¦, π§. And weβre told that this point lies in the π₯π¦-plane. We need to use this information to determine the π§-coordinate of our point. Thereβs a few different ways of answering this question. One way is to look at this graphically. Letβs start by recalling what it means for a point to be on the π₯π¦-plane graphically. The π₯π¦-plane is the set of all points which we get by taking π§-coordinate equal to zero.
Essentially, weβre just letting the π₯-coordinate or the π¦-coordinate be whatever they want. However, the π§-coordinate has to be equal to zero. So in particular, if π is any point on our π₯π¦-plane, π will have the form π, π, zero, where π and π can be any real number. And we can use this to determine the π§-coordinate of the point given to us in the question. We know the π§-coordinate of any point on the π₯π¦-plane is zero. So the π§-coordinate of the point given to us in the question must be equal to zero.