WEBVTT

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Here is the problem: Find the cross product of ⟨2, 1, negative 1⟩ and ⟨3, negative 2, 4⟩.

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Cross product of two 3D vectors.

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Write the determinant with unit vectors i, j, k in the first row.

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i component.

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j component (note the minus sign in the expansion).

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k component.

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Magnitude equals area of the parallelogram spanned by u and v.

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Check orthogonality.

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So the answer is u times v equals ⟨2, negative 11, negative 7⟩.

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The result is perpendicular to both u and v; its length the square root of 174 approximately 13.19090596 is the area of the parallelogram they span (the triangle has half that area).

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The result is perpendicular to both input vectors (both dot products are 0).