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quiz2_sol

# quiz2_sol - the parallelogram determined by-→ OA and-→...

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Solutions of CalcIII Quiz 2 September 20, 2006 1. The volume is the absolute value of the determinant - 3 0 1 - 2 1 1 1 1 1 which is 6 2. Let us assume D has coordinates ( x 0 , y 0 , z 0 ). The volume is the absolute value of the determinant - 3 0 1 - 2 1 1 x 0 y 0 z 0 which is x 0 + 2 y 0 + 3 z 0 . Since D is on the plane x + 2 y + 3 z = 6, we have x 0 + 2 y 0 + 3 z 0 = 6. 3. The volume of the parallelepiped is given by the product of the area of
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Unformatted text preview: the parallelogram determined by-→ OA and--→ OB and its height. Both A and B are on the plane x + 2 y + 3 z = 0 to which x + 2 y + 3 z = 6 is parallel. Therefore, for any point D on the plane x + 2 y + 3 z = 6, the height of the parallelepiped is the same. 1...
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