Quiz0904 PDF

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MATH 241 Quiz Due 09/04/2020

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Instructions: You can fill this out digitally, or you can print and scan, or you can simply write your answers on a separate piece of paper and scan that. 1. If the points (1, 0, 3) and (8, 3, 3) are on opposite sides of a sphere, what is the center of the sphere and what is its radius?

2. Let P = (1, 2, 2) and Q = (3, −4, 5). Consider the set of points whose distance to P is twice the distance to Q. Show that this set of points is a sphere and find its center and radius. Hint: Suppose the distance from (x, y, z) to P is twice the distance to Q. Write down an equation which states this and manipulate the equation.

3. Sketch the following sphere and mark the top and bottom points with their coordinates: x2 + y2 + z 2 + 2y − 6z = 6

4. Let u ¯ = 2 i − 4 j + 7 k . Find a vector of length 12 pointing in the opposite direction from u ¯.

5. Let v = 5 i + 5 j + 5 k and w = −10 i − 15 j − 10 k Explain why these vectors are not parallel....