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**Unformatted text preview: **plane, the distance formula along any vertical or horizontal line, and the Pythagorean Theorem. Use these tools to derive the distance formula between the arbitrary points P and P 1 . P_0 P_1 Problem 13.1.2 Now that we have a distance formula for 3-space, what should the deFnition of a sphere with radius r > and center ( h, k, l ) be? Problem 13.1.3 Describe the sphere with equation 2 x 2 + 2 y 2 + 2 z 2 =-20 x + 12 y-4 z-52 . Problem 13.1.4 Describe the set of points that satisfy x 2 + y 2 + z 2 ≤ 4 . Problem 13.1.5 ±ind an equation of the set of points that are equidistant from the points A (1 , 2 , 3) and B (-1 , 4 , 7) . What does this set of points look like? 1...

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