A parallelepiped is a three-dimensional figure like a cube except that the faces

Question

A parallelepiped is a three-dimensional figure like a cube except that the faces are not rectangles but are parallelograms, but the sides bounded by B and C and the sides bounded by A and C are rectangles. If the angle Theta were 90 Degree , the faces would all be rectangles, and the object would be called a cuboid. We define three of the sides of the parallelepiped as vectors A, B, and C as shown. In terms of these vectors, what is the volume of the object? Can you express your answer in terms of the products of the vectors?(Hint: how do you calculate the area of a parallelogram using vectors?)

Explanation / Answer

Volume of the object V = A . ( B X C ) where B X C = cross product of vectors B and C A . ( B X C ) = Dot product of vector A and crossproduct of vectors B ,C
Area of the parallelogram A = 2 [ ( A X B ) + ( B X C )+ ( C X A ) ] where B X C = cross product of vectors B and C           AX B = cross product of vectors A and B          C X A = cross product of vectors C and A

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