Q. 14

Mark against the A. 7x + 5y – 4z – 8 = 0

B. 7x – 5y + 4z – 8 = 0

C. 5x – 7y + 4z – 8 = 0

D. 5x + 7y – 4z + 8 = 0

Answer :

Given: Plane passes through the intersection of planes 3x – y + 2z – 4 = 0 and x + y + z – 2 = 0. Point A(2, 2, 1) lies on the plane.


To find: Equation of the plane.


Formula Used: Equation of plane passing through the intersection of 2 planes P �1 and P2 is given by P1 + λP2 = 0


Explanation:


Equation of plane is


3x – y + 2z – 4 + λ (x + y + z - 2) = 0 … (1)


Since A(2, 2, 1) lies on the plane,


6 – 2 + 2 – 4 + λ (2 + 2 + 1 – 2) = 0


2 + 3λ = 0



Substituting in (1) and multiplying by 3,


9x – 3y + 6z – 12 – 2 (x + y + z - 2) = 0


9x – 3y + 6z – 12 – 2x – 2y – 2z + 4 = 0


7x – 5y + 4z – 8 = 0


Therefore the equation of the plane is 7x – 5y + 4z – 8 = 0

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