Step 1:

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The plane passes through the point $\"\"$ .

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The plane equations are \ \

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$\"\"$

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$\"\"$

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The cross product of two normal vectors is the direction vector for the line of intersection.

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The normal vectors of two planes are

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$\"\"$

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$\"\"$ .

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The cross product of two vectors is

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$\"\"$

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$\"\"$

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The direction vector of line of intersection is $\"\"$ .

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Step 2:

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Find the point lies in line of intersection, set $\"\"$ .

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

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$\"\"$

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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The point lies in line of intersection is $\"\"$ .

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Step 3:

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Find the point lies in line of intersection, set $\"\"$ .

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

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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The point lies in plane of intersection is $\"\"$ .

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Let $\"\"$ be the vector from $\"\"$ to $\"\"$ .

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$\"\"$ .

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Let $\"\"$ be the vector from $\"\"$ to $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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The plane equation is $\"\"$

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$\"\"$

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.The plane equation is

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$\"\"$

\

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The plane equation is $\"\"$ .

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$\"\"$

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The plane equation is

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Step 3:

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The plane parallel to the line of intersection is $\"\"$ .

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Let $\"\"$ be the vector from $\"\"$ to $\"\"$ .

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$\"\"$

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The direction vector of line of intersection is $\"\"$ .

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The line of intersection is cross product of $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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The normal vector is $\"\"$ .

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The plane equation is $\"\"$

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$\"\"$

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The plane equation is $\"\"$ .

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Solution:

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The plane equation is $\"\"$ .

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$\"\"$

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\