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

$ 1 \le x^2 + y^2 + z^2 \le 5 $

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every point on or between the two spheres of radius 1 and radius $\sqrt{5},$ bothcentered at the origin

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Kyle Parsotan

May 12, 2020

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Johns Hopkins University

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Baylor University

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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All right. So notice here, this X squared plus y squared plus z squared is a sphere. So we're bounding a sphere by two different rady I So this is a sphere with radius equaling square two five and radius equaling one. So it's going to be this sphere and a little bit of it. There's going to be cut it out.

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