Step 1:

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The vector line equations are $\"\"$ and $\"\"$ .

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Find the intersection of the two lines, by equating two lines.

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$\"\"$

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$\"\"$

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$\"\"$ .

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Equating $\"\"$ terms:

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$\"\"$

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$\"\"$ .

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Equating $\"\"$ terms:

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The position vector is $\"\"$ .

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Checking:

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .