Vectors in Space

Category: Mathematics

Part 1The Sphere:  In space, the collection of all points that are the same distance from some fixed point iscalled a sphere.See the illustration below. The constant distance is called the radius, and the fixed point is the center of thesphere. Show that the equation of a sphere with the center at (x0, y0, z0) and the radius r is(x – x0)2 + (y-y0)2 + (z-z0)2 = r2[Hint: Use the distance Formula.]   Part 2Consider the following vectors u and v: IF and what, if anything, can you conclude about the vectors u and v?Discuss your conclusion in detail.   Your response must be a minimum of 100 word for both questions.

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