A parallelogram is formed in R^3 by the vectors PA=(3, 2, -3) and PB=(4, 1, 5). The point P=(0, 2, 3) Find the area of the parallelogram.
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One side of the parallelogram is the vector PA and another is PB. Let the fourth vertex be C.
The vertex A is (0, 2, 3) + (3, 2, -3) = (3, 4, 0)
The vertex B is (0, 2, 3) + (4, 1, 5) = (4, 3, 8)
The fourth vertex C is A + PB = (7, 5, 5)
Now, the diagonals of the parallelogram are:
AB = (3, 4, 0) - (4, 3, 8) = (-1, 1, -8). |AB| = sqrt...
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