WEBVTT

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Here is the problem: Find the magnitude and unit vector of ⟨2, negative 1, 3⟩.

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Vector magnitude and unit vector using exact components.

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Square the components and add them.

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Take the square root for the magnitude.

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Divide each component by the magnitude for the unit vector. The denominators are rationalised, so each component is written with the square root on top.

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Check: the unit vector has length 1.

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So the answer is |u| equals the square root of 14 approximately 3.741657387; unit vector û equals ⟨the square root of 14 over 7, negative the square root of 14 over 14, 3the square root of 14 over 14⟩.

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Vectors are added, subtracted and scaled one component at a time. The magnitude comes from the Pythagorean theorem, and dividing by it gives a unit vector of length 1 pointing the same way.

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The unit vector prime s components square and add to 1.