Verify that the cross product of two vectors is anticommutative by using their component definitions.

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Anticommutativity of the Cross Product

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Verify that \( \mathbf{B} \times \mathbf{A} = - (\mathbf{A} \times \mathbf{B}) \).

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What you need first

Definition of the cross product in terms of components
Basic algebraic manipulation
Scalar multiplication of vectors

What this problem tests

Tests the student's ability to apply the component definition of the cross product and perform basic algebraic manipulations to prove a vector identity.

This is a fundamental property of the cross product introduced early in multivariable calculus and vector algebra courses.

Anticommutativity of the Cross Product

What you need first

What this problem tests

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