Prove a vector identity involving the cross product of the sum and difference of two vectors.

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Cross Product of Sum and Difference of Vectors

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Prove \( (A - B) \times (A + B) = 2(A \times B) \).

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What you need first

The definition of the cross product
The distributive property of the cross product
The anticommutative property of the cross product

What this problem tests

Tests the student's ability to correctly apply the distributive and anticommutative properties of the cross product, and to remember that the cross product of a vector with itself is zero.

This is a standard introductory problem in multivariable calculus or linear algebra courses when learning the algebraic properties of the cross product.

Cross Product of Sum and Difference of Vectors

What you need first

What this problem tests

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