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Draw the following direction and plane in the cubes (10 points)(2 I0)[2 12]...

Question

Draw the following direction and plane in the cubes (10 points)(2 I0)[2 12]

Draw the following direction and plane in the cubes (10 points) (2 I0) [2 12]



Answers

Sketch the plane represented by the linear equation. Then list four points that lie in the plane. $$3 x+2 y+2 z=12$$

So when we're sketching the graph of a plane, something that we can do is we can uh graph the plane by looking at different points. So for example, in this case if we let X equal zero, we're going to end up if we let um y and Z equals zero will get the 00.600 So what we can do is graph 0.600 Then if we it's not gonna be an equation that would just be a point or have 600 um okay we'll have that point there and then we know that if we have to let X and Z equals zero, then we'll get 0 to 00 point. Yeah. And then lastly if we let uh X and white blue zero will get 004 as a point. So we see that this will create the plane that we have if we connect these and then essentially allow them to create the rest of our plane. Mhm.

Alright problem 4 31 with a physical to one half. Come on to x Here's the vector field.

So in the xz plane, do I coordinate is given by zero. So we would replace why? By zero and the given equation. So we have X squared plus zero azar. Why minus four Squared plus Z minus three squared 2144. Now we use a 16 from the 14 over here. You can take it over from D 1 34 So we end up with X squared plus Z minus three squared equal to 1 44 minus 16 which is on 28. Well, then know that the radius is equal to Route 1 28 and that in the xz plane it is centered hat 003 Moving on to the trace with Z being equal. Negative two. We now know that Z coordinate everywhere is negative two. So we do the above again. But we have X squared plus y minus four instead of Syria this time because we're in the seaplane, then this is negative. Two minus three. Not is he and then that is equal to 1 44 We can then subtract out the 25 from here and on the other side to get 1 19 So we would then know that radius is equal to 19 and we also know that the center is going to be out. It's not parentheses there. The center is going to be at zero for secret.

So in this problem we're given this equation and were asked to sketch the plane. Yeah, representing this equation. And then are asked to list four points four points on this plane. All right. So, first of all the way to sketch this is two. Figure out the X coordinate when Y and Z or zero, and then the Y coordinate went X and Z or zero. And the Z coordinate went X and Y are zero. In other words, the three intercepts that happened well, when Why? and 00 and I have two, X equals 12. And so X equals six. So that means I have 600. So that's one of the points on this plane in it. So, let's list that over here. That's one of the points on this plane. And that means on the x axis here and go 123456. So, I'll have point there. Okay, then, when X and 00 I have three, y equals 12. So why is four? So now I have another point here at zero for 0. Okay. So why is four so 1234 at that point there? So that means the plane's gonna intersect that line. I can do a little bit better drawing that line. Let me see here. Yeah. Almost there we go. And intersect that line. Okay? So now when X&Y are zero four z equals 12. one x 4. See his three. All right, so there's another .003. All right, so 123. No they're sick that point right there. So oh that missed pretty badly. Let me redo that. What's that one? That sign And then there's that sign. So there's the plane drawn there for us and now we need one more point. All right, So let's let x. equal one and y equal to what happens when X is one? That means I have two times one is two. Was Why is 2? So three times 2 is six Plus four. Z equals 12. Six plus two is eight plus four. Z equals 12. It's attract eight four. Z equals four, So z equals one. So here's the 4.1, two, one. There's four points on our plane and our plane is drawn over there on the left hand side.


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