$\"\"$

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The line passes through the points $\"\"$ and $\"\"$ and intersect the plane at $\"\"$ .

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The vector equation of a line segment passing through points with position vectors $\"\"$ and $\"\"$ is $\"\"$ .

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The vector $\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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The parametric equations are $\"\"$ , $\"\"$ and $\"\"$ .

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The equation of the plane is $\"\"$ .

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If the line intersect the plane, then $\"\"$ , $\"\"$ and $\"\"$ satisfy the equation of the plane.

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in parametric equations.

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

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

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The point of intersection is $\"\"$ .

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$\"\"$

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The point of intersection is $\"\"$ .