# 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). - Mathematics and Statistics

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).

#### Solution

The equation of plane passing through the intersection of the planes 3x + 2y – z + 1 = 0 and x + y + z – 2 = 0 is

3x + 2y – z + 1)+lambda( x + y + z – 2)=0        ...........(1)

It passes through the point (2, 2, 1)

(6+4-1+1)+lambda(2+2+1-2)=0

10+3lambda=0

lambda=-10/3

Now,

(3x+2y-z+1)+(-10/3)(x+y+z-2)=0   .......[from(1)]

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

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

The equation of plane is x+4y+13z=23

Concept: Plane - Equation of Plane Passing Through the Intersection of Two Given Planes
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