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Find an equation of the sphere that passes through the origin and whose center is $ (1, 2, 3) $.

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Harvey Mudd College

Baylor 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.

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.

02:08

Find an equation of the sp…

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01:26

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Find an equation of a sphe…

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02:40

find an equation spared passes through the region and whose center is 123 Okay, we have no the center. But we do know this. The radio's so we're first gonna write down the equation like this. X minus one plus Y minus two. Square one is two and square Z minus three. Because our square what is are the c. R s over radios. Really? Is, uh, this fair? Yeah. And, uh, okay, it passes through the region so we can plug in according to the our region. And the equation holds. What does it mean? So if you plug in 000 it's going to be one square plus two square, three square equals are square. So, uh, Oscar is going to be one plus four plus 9. 14. Good. So now we have known Oscars 14. We're gonna replace it here, so, uh, square equals because 14. Yeah, and final equation is this. That's just one square plus women's to square. Plus, the mystery square equals equals 14

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