Find the cross product of two given 3D vectors and express the result using standard unit vectors.

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Computing the Cross Product of Two Vectors

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Find \( \mathbf{p} \times \mathbf{q} \) for \( \mathbf{p} = \langle 5, 1, 2 \rangle \) and \( \mathbf{q} = \langle -2, 0, 1 \rangle \). Express the answer using standard unit vectors.

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What you need first

Evaluating 2x2 and 3x3 determinants
Understanding vector notation and components
Familiarity with standard unit vectors i, j, k

What this problem tests

Tests the ability to correctly set up and evaluate the determinant for a cross product, including managing the alternating signs.

This is a fundamental operation in multivariable calculus and physics, often used to find a vector orthogonal to two given vectors.

Computing the Cross Product of Two Vectors

What you need first

What this problem tests

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