WEBVTT

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Here is the problem: Find the cross product of ⟨-2, 3, 1⟩ and ⟨4, 0, negative 5⟩.

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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 ⟨-15, negative 6, negative 12⟩.

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The result is perpendicular to both u and v; its length 9the square root of 5 approximately 20.1246118 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).