WEBVTT
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If the vector π is equal to two, negative five, two, find the magnitude of π.
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Remember, this notation is asking us to find the magnitude of π.
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Thatβs the distance between an initial point and the end point at π.
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This is a position vector.
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So weβre looking to find the distance between π and the origin.
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And thereβs a formula we can use.
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Itβs an extension of the Pythagorean theorem.
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And it says that the magnitude of a vector π£ given by π₯π plus π¦π plus π§π or π₯, π¦, π§ is given by the square root of π₯ squared plus π¦ squared plus π§ squared.
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Letβs substitute what we know about our vector π into the formula.
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π₯ is two.
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π¦ is negative five.
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And π§ is also two.
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So the magnitude of π is the square root of two squared plus negative five squared plus two squared.
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Two squared is four.
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And negative five squared is 25.
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So the magnitude of π is found by the square root of four plus 25 plus four, which is 33.
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So the magnitude of π is root 33.