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Describe in words the region of $\mathbb{R}^{3}$ represented by the equation(s) or inequalities.$x^{2}+y^{2}+z^{2} \leqslant 4$

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Missouri State University

Campbell University

University of Michigan - Ann Arbor

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, what we have here is a sphere: you have this x, minus a square plus y minus b, squared plus z, minus c squared equals r square, that is standard form for a sphere of center, a b c and radius r. So here then, what i have is a sphere center, the origin. The a b c will be 000 point. So is a sphere center origin of 000 and radius. L 4 is the r squared. So is 2 point. Now we are less than or equal to 4. So that means my answer will be any point on or inside this sphere, so any point on the surface or inside the sphere of radius to center 000 point: that's the answer.

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