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

$ x^2 + y^2 = 4 $, $ z = -1 $

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$x^{2}+y^{2}=4, z=-1$ is a circle with radius 2 and center $(0,0,-1)$ lying onthe plane $z=-1$

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Johns Hopkins University

Missouri State University

Baylor University

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.

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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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Describe in words the regi…

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Okay, so if we take a look at this here, if we look at this picture in the X Y plain, this part is a cylinder Dillinger. But on ly at Z equals negative one. So it's taking one slice of a cylinder. So one slice of cylinder and one slice of a cylinder is a circle. So it's a circle, uh, down here with the radius one at Z equals negative one.

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