I need help please on this question A plane passes through the point (1,1,1) and is perpendicular to each of the planes 3x−2y+3z+6=0 and 6x−2y−3z−6=0. Find its equation.

Inbrunstlr 2022-10-03 Answered
A plane passes through the point (1,1,1) and is perpendicular to each of the planes
3x−2y+3z+6=0 and 6x−2y−3z−6=0. Find its equation. The problem is I don't have an idea of the concept. All I know is that the normal of first equation is (3,−2,3) and that of the second is (6,−2,−3).
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Answers (2)

Dayana Powers
Answered 2022-10-04 Author has 6 answers
Here’s a hint:
the normal of the third plane is perpendicular to both normals of the two given planes.
Use the cross product.
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kasibug1v
Answered 2022-10-05 Author has 4 answers
So if T(x,y,z) is in this plane and A(1,1,1) then
A T = ( x 1 , y 1 , z 1 ) = m ( 3 , 2 , 3 ) + n ( 6 , 2 , 3 )
for some scalars m,n. Eliminate the scalars and you are done.
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