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Numerade Educator



Problem 36 Medium Difficulty

Describe in words the region of $ \mathbb{R}^3 $ represented by the equation(s) or inequality.

$ x = z $


a plane that contains the $y$ -axis and is perpendicular to the $x z$ -plane


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Video Transcript

Okay, So our question is to find the region and our three, though just three d say three xx, sis, You're y axis new Z axis, That's where absented by exa Guilty. So all the points in this three d space where your ex co ordinate eagles here Z quarter in it and we want to explain what that means in words. So an easy way to think about this is to think about something you already know really well. And I'm sure all of you know, um X equals why that line in Judy Say so and are too. And we know that this looks like you have your to de Grasse and it just all the points where X equals y really simple. You're diagonal line, and so we can kind of bring that same concept over here to where you have your three d space. And you know that all of your ex Val using equal yours eve out is in the same way that your ex values you call your y values. In the previous example, we were just draw that same line changed color. We draw that theme line over here. But that's all because it's three d space. This can actually continue, um, to form a plane. So even if I move up a little bit right here just changing my wife cord in it, my ex still equals my Z. And the same is over here if I move down the of the same thing. So you actually end up performing a plane with all these valleys where X equals e, and it's only or why that's changing. So because on Lee, or why that's changing, you actually end up containing this entire axis in your plane. And another key characteristic of this plane is that it's perpendicular two. You're X the plane. So this is your XY plane here? Never particular.