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Use intercepts to help sketch the plane.

$ 6x - 3y + 4z = 6 $

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$6 x-3 y+4 z=6$

01:52

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 5

Equations of Lines and Planes

Vectors

Missouri State University

Baylor University

University of Nottingham

Boston College

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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Use intercepts to help ske…

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Find all intercepts and sk…

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Find the intercepts and sk…

So if we want to sketch this plane here, they tell us to use the intercepts to help us. Let's go ahead and do that first. So we're going to first do so to find the X intercept. We're going to set y and Z equal to zero. And so if we do that when it was six x 06 which is telling your sex is one. Now, if we want the why intercept, we're going to set X and Z equal to zero, which would give us negative three. Why is it for six? So why is going to be? It looks like a negative, too. And then, lastly, to get our Z intercept, we're going to set X and Y equal to zero. And so that would give us four. Z is equal to six, which is going to say Z is equal to 1.5 and actually let me go ahead and make the screen a little bit bigger. So let's come over here and put down or grid. So this is X. This is why, and this is C So 123451234512345 Wow. So first, our X intercept is going to be at X 0 to 1. So it's just going to be right here. Why is going to be at negative two? So we're going to go to backwards, because remember, these are supposed to be the positive. So 12 it will be somewhere around here, and then Z 0 to 1.5 is going to be right here. So these are going to be our intercepts. And so now we can go ahead and just draw our plan. So what I would normally do to kind of help, uh, is just draw lines going through all of these first kind of like this, and then you can kind of just extend out because we know all these lines should be in the same plane. You gotta do something kind of like with this. And then this kind of creates our plane. Uh, and if you want, you could go ahead and actually like a race. All of these lines here. Yeah, if you want just to kind of make it look more like a plane or at least make it look a little bit better, But it's also not really needed. So I just kind of depends on what you would like. So you can either leave it like this here, or you could, uh, keep all those lines drawn in there like we had before. But, I mean, regardless of how you draw, you still end up getting your plane.

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