Question

find the equation of a plane through the point - 1, - 1, 2 and perpendicular to the plane 3 X + 2 Y - 3z=1 AND 5x-4y+z= 5​

Answer 1

I hope it will be answer of your question

Answer 2

Explanation:-

Equation of any plane passing through the point (-1,-1,2) is

A(x+1) + B (y+1) +C (z-2) =0. —--(1)

As plane (1) is perpendicular to the planes

3x+2y-3z=1 and 5x-4y+z =5,we get

⇒3A +2B-3C=0 —--(2)

⇒5A -4B +C =0 —--(3)

On solving (2) and (3) for A, B, C, we get:-

A : B : C = 5 : 9 : 11

On Substituting these value of A,B,C in (1), we get:-

➠5 (x+1)+9 (y+1)+11 (z-2)=0

➠5x+9y+11z-8 =0

Which is the required plane.