$\"\"$

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

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The plane equation is $\"\"$ .

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The vector equation for the parametric equation is $\"\"$ .

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Find $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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The normal plane at point is normal to the vector $\"\"$ at the same point.

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The plane equation is $\"\"$ .

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Normal vector to the plane $\"\"$ is $\"\"$ .

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The normal vector to the plane is $\"\"$ .

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$\"\"$

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Normal vector to the plane is parallel to the plane $\"\"$ .

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Parallel vector is $\"\"$ .

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Equate the vector coefficients.

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

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

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Substitute $\"\"$ .

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

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

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

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Therefore, $\"\"$ .

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

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Substitute $\"\"$ .

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

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

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Therefore the point is $\"\"$ .

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$\"\"$

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The point is $\"\"$ .