WEBVTT

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Here is the problem: Find the dot product and the angle between ⟨3, 4⟩ and ⟨-4, 3⟩.

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Dot product of two 2-dimensional vectors.

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Multiply matching components.

4
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Add the products.

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Find the magnitudes.

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Angle between the vectors.

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Scalar and vector projection of u onto v.

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So the answer is u times v equals 0, angle approximately 90°.

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The dot product is 0, so the vectors are orthogonal (perpendicular).

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Computed exactly; the dot product is symmetric, so v times u gives the same value.