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Describe and sketch the surface.$$y^{2}+z=4$$

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Calculus 3

Chapter 11

Vectors and the Geometry of Space

Section 6

Surfaces in Spacee

Vectors

Johns Hopkins University

Missouri State University

Campbell University

Harvey Mudd 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.

01:47

Describe and sketch the su…

01:11

0:00

04:29

00:56

for this problem, we are asked to sketch and describe the surface described or given by why squared plus Z equals four. So to begin, we can note that we don't have anything telling us what X is doing. But in the Y. Z plane we can write this as equals four minus Y squared. So we would expect that in that plane 1 2nd here. I'll say that that's why coming out of the page is X. And then Z. So in the Y. Z plane we would expect to have something that looks like a downward opening parabola, Where when y equals zero, z equals four. So we'd expect to have something like this where it's opening downwards. But since we don't have anything telling us about what X is doing well, X or our parabola is going to be looking unchanged as X varies. So we'll have just this sort of, I believe it's technically referred to as a kind of cylinder continuing with a parabolic cross section lying along the X axis.

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