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Problem 47 Medium Difficulty

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 $.

Answer

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

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Video Transcript

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.