$\"\"$

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Vector equation of the plane $\"\"$ with the point $\"\"$ and normal vector $\"\"$ is $\"\"$ .

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$\"\"$

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The plane that passes through the point $\"\"$ and $\"\"$ and is perpendicular to the line $\"\"$ .

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The two points $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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The line $\"\"$ is perpendicular to the plane.

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Hence the normal vector is vector $\"\"$ . $\"\"$

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Since $\"\"$ and $\"\"$ lie in the same plane ,the cross product is orthogonal to the that plane and it can be represented as perpendicular vector $\"\"$ .

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$\"\"$

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$\"\"$

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Hence the vector $\"\"$ .

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$\"\"$

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Vector equation of the plane $\"\"$ with the point $\"\"$ and normal vector $\"\"$ is $\"\"$ .

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

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Substitute above values in vector equation formula.

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$\"\"$

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Therefore, the equation of the plane is $\"\"$ .

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$\"\"$

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