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

$ 2x^2 + 2y^2 + 2z^2 = 8x - 24z + 1 $

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$(2,0,-6), 9 / \sqrt{2}$

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

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University of Nottingham

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.

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.

07:41

Show that the equation rep…

0:00

03:37

02:22

01:18

01:58

05:03

05:30

02:16

01:06

06:50

right. So we're going to complete the square. So, uh, he's do these guys over, okay? And then we do the completeness. Where? Algorithm. Okay, so we get to times X minus two. Squared was to y squared. It was two times he mighta six square. That's all going to be equal to eighty one here. So you want over eighty one over to sew. The center is at two zero six the radius, his nine overact.

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