Prove that the vector triple product of three mutually perpendicular vectors is the zero vector.

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Vector Triple Product of Mutually Perpendicular Vectors

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If \( \mathbf{A} \), \( \mathbf{B} \), \( \mathbf{C} \) are mutually perpendicular, show that \( \mathbf{A} \times (\mathbf{B} \times \mathbf{C}) = \mathbf{0} \).

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What you need first

Definition of the cross product
Geometric interpretation of the cross product
Properties of mutually perpendicular vectors in 3D space

What this problem tests

Tests the geometric understanding of the cross product, specifically its orthogonality to the operands and its behavior with parallel vectors.

This is a standard introductory problem in multivariable calculus and vector algebra, testing geometric intuition over algebraic expansion.

Vector Triple Product of Mutually Perpendicular Vectors

What you need first

What this problem tests

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