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

Inbrunstlr

Answered question

2022-10-03

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).

Answer & Explanation

Dayana Powers

Dayana Powers

Beginner2022-10-04Added 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.
kasibug1v

kasibug1v

Beginner2022-10-05Added 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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