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Show that a. (b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors, a, b and c.

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Show that a. (b × c) is equal in magnitude to the volume of the parallelepiped formed on the three vectors, a, b and c.
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Best answer

A parallelepiped with origin O and sides a, b, and c is shown in the following figure.

Let cap n be a unit vector perpendicular to both b and c. Hence, cap n and a have the same direction.

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