Find the volume of a parallelepiped defined by three vectors originating from the origin.

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Volume of a Parallelepiped from Three Vectors

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Find the volume of the parallelepiped whose edges are \( \vec{OA} \), \( \vec{OB} \), \( \vec{OC} \), where \( O = (0, 0, 0) \), \( A = (1, 2, 3) \), \( B = (1, 1, 2) \), \( C = (2, 1, 1) \).

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What you need first

Vector notation and coordinates
Computing the cross product of two 3D vectors
Computing the dot product of two vectors
Evaluating 3x3 determinants

What this problem tests

Tests the ability to compute cross and dot products and apply them to find geometric volumes.

This is a standard problem in multivariable calculus and linear algebra courses, introducing the geometric interpretation of the scalar triple product and determinants.

Volume of a Parallelepiped from Three Vectors

What you need first

What this problem tests

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