$\"\"$

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The parametric equations of the line 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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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 $\"\"$ .