Find the volume of the parallelepiped formed by the vectors U(3,-2,5), V(2,2,-1) and W(-4,3,2).?
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confuse how to get the solution??...
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Answer:
the volume of a parallelepiped is simply the product Volume=|U dot (V X W)| <- where X is the cross product so do the cross product of V and W | i j k| | 2 2 -1| = i (2*2 - 3*(-1)) - j (2*2 - (-4)*(-1)) + k (2*3 - (-4)*2) = i (4+3) - j (4+4) +k (6+8) | -4 3 2| = 7i - 8j + 14k U dot < 7, 8, 14> = < 3, -2, 5> dot <7, 8, 14> = (3*7) + ((-2)*8) + (14*5) = 21 - 16 + 70 = 75
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