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Show that the equation represents a sphere, and find its center and radius.

$ x^2 + y^2 + z^2 - 2x - 4y + 8z = 15 $

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Oregon State University

Harvey Mudd College

Baylor University

University of Nottingham

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.

05:03

Show that the equation rep…

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03:00

Show that the equation x 2…

01:51

Show that x2 + y2 + z2 = 1…

05:30

02:45

02:16

03:37

02:18

$15-18$ Center and Radius …

01:23

Center and Radius of a Sph…

01:18

01:37

$15-18$ Show that the equa…

03:50

So the way that we're going to do this is by using completing the square. So ahh. Completing the square here. Not too difficult to see. Hey, um, get something that looks like that. And then well, we just to write this stuff out and then we got nine is twenty one single toe five. Right. This stuff out right here. So the center that one too negative for in the radius of six.

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