Finding the Volume of a Pyramid Using Vectors

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The volume of a pyramid is

In three dimensional space all the vertices of the pyramid can be given coordinates.

The bass area can be expressed as the cross product of the vectorsand

The To find the height of the pyramid, notice that the cross product of two vectors is perpendicular to both vectors.anddefine the base of the pyramid, sois perpendicular to the base, and in the direction of the height. The height will be given by the component ofin the direction of the unit vectorThis is equal to

Then

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