Let P be the parallelepiped bounded by the three pairs of pa
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Let P be the parallelepiped bounded by the three pairs of parallel planes a r D 0, a r D d1 > 0, b r D 0, b r D d2 > 0,
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Let P be the parallelepiped bounded by the three pairs of parallel planes a r D 0, a r D d1 > 0, b r D 0, b r D d2 > 0, c r D 0, and c r D d3 > 0, where a, b, and c are constant vectors, and r D xi C yj C zk. Show that ZZZ P .a r/.b r/.c r/ dx dy dz D .d1d2d3/2 8ja .b c/j: Hint: Make the change of variables u D a r, v D b r, w D c r.
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