#### Question

Find the equation of the plane passing through the intersection of the planes: x + y + z + 1 = 0 and 2x -3y + 5z -2 = 0 and the point ( -1, 2, 1 ).

#### Solution

Equation of required plane passing through the intersection of the planes x + y + x + 1 = 0

and 2x - 3y + 5y - 2 = 0 is

`(x + y + z + 1) + lambda (2x - 3y + 5z - 2) = 0` .....(1)

It passes through (-1, 2, 1)

∴ `(-1 + 2 + 1 + 1) + lambda(-2 - 6 + 5 - 2) = 0`

`3 + lambda(-5) = 0`

`lambda = 3/5`

In equation (1)

`(x + y + z + 1) + 3/5 (2x - 3y + 5z - 2) = 0`

`5x + 5y + 5z + 5 + 6x - 9y + 15 z - 6 = 0`

11x - 4y + 20z - 1 = 0

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#### APPEARS IN

Solution Find the Equation of the Plane Passing Through the Intersection of the Planes: X + Y + Z + 1 = 0 and 2x -3y + 5z -2 = 0 and the Point ( -1, 2, 1 ). Concept: Intersection of the Line and Plane.