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Describe and sketch the surface.$$x^{2}-y=0$$

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Calculus 3

Chapter 11

Vectors and the Geometry of Space

Section 6

Surfaces in Spacee

Vectors

Missouri State University

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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.

01:44

Describe and sketch the su…

01:27

01:11

00:56

02:16

For this problem, we are asked to describe and sketch the surface defined by x squared minus Y equals zero. Alternatively, we can write this as well, it would be defined by Y equals X squared where Z is not specified. So in the xy plane we would expect to have something that looks like a parabola and then we would expect it to not vary as we go along Z. So in X and y we have a parabola and then well that parabola is just going to be extending upwards and downwards where the cross section should always look identical. So probably our surface then should look something like this kind of tricky to draw. I believe that this would be defined technically as being a kind of cylinder.

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