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44 votes
44 votes
Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x 3y − z = 0.

User Alaa Sadik
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1 Answer

16 votes
16 votes

The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to
2x+3y-z=0 is the vector (2, 3, -1), since
(2,3,-1)\cdot(x,y,z)=0.

Then the plane we want has equation


(2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}

User Luca Carlon
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3.1k points