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If $ r = \langle x, y, z \rangle $ and $ r_0 = \langle x_0, y_0, z_0 \rangle $, describe the set of all points $ (x, y, z) $ such that $ \mid r - r_0 \mid = 1 $.

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$$\left|r-r_{0}\right|=\sqrt{\left\langle\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}+\left(z-z_{0}\right)^{2}>\right.}=1$$equation of the unit sphere

01:41

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Oregon State University

University of Michigan - Ann Arbor

Idaho State University

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.

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So for this problem we know that R equals X, Y. Z. And are not equals X. Not why not peanut describes all of the set of the points X. Y. Z. Such that ar minus why not absolute value is going to be equal to one? So we want to know what that's going to be. Well, we know that um in this case that the absolute value is going to be one, so that means that the distance from our two are not as one. So the distance from our or not okay Going to be equal to one and are and are not are vectors. So we know that are not is going to be this single point and we have all the points, all the vectors from that point. So it's going to mean that this is going to be a spear and in this case it's the unit sphere because we know it only has a radius of one. Yeah.

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