$\"\"$

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The vectors are $\"\"$ , $\"\"$ and $\"\"$ .

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Show that $\"\"$ .

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Let $\"\"$ be the point on the line segment $\"\"$ that is twice as far from $\"\"$ as it is from $\"\"$ .

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Draw the related figure:

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$\"\"$

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From the figure :

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$\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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Substitue $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Consider $\"\"$

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Substitue $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Since $\"\"$ .

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ .

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$\"\"$

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$\"\"$ .