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