Question

Find the equation of the plane passing through the intersection of the planes 3x + 2y - z + 1 = 0 and x + y + z - 2 = 0 and the point (2, 2, 1).

Answer 1

Answer:

Equation of plane

x+4y+13z-23=0

Step-by-step explanation:

To find the equation of the plane passing through the intersection of the planes 3x + 2y - z + 1 = 0 and x + y + z - 2 = 0 and the point (2, 2, 1).

We know that standard eq of plane passing through plane P1 and P2 is

P1+λ P2 =0

3x + 2y - z + 1 +λ( x + y + z - 2) = 0

since the plane psiing through the points(2,2,1) ,so it satisfies the  above equation

3(2)+2(2)-1+1+λ(2+2+1-2)=0

6+4+3λ=0

λ=-10/3

Now put the value of λ in the equation discussed above,so

3(3x + 2y - z + 1) -10( x + y + z - 2) = 0

9x+6y-3z+3-10x-10y-10z+20=0

-x-4y-13z+23=0

x+4y+13z-23=0