Q. 15

Mark against the A. 4x + 3y – 2z – 3 = 0

B. 4x – 3y + 2z + 3 = 0

C. 4x – 3y + 2z – 3 = 0

D. None of these

Answer :

Given: Plane passes through A(0, -1, 0), B(2, 1, -1) and C(1, 1, 1)


To find: Equation of the plane


Formula Used: Equation of a plane is


a(x – x1) + b(y – y1) + c(z – z1) = 0


where a:b:c is the direction ratios of the normal to the plane.


(x1, y1, z1) is a point on the plane.


Explanation:


Let the equation of plane be a(x – x1) + b(y – y1) + c(z – z1) = 0


Substituting point A,


ax + b(y + 1) + cz = 0 … (1)


Substituting points B and C,


2a + 2b – c = 0 and a + 2b +c = 0


Solving,




Therefore, a : b : c = 4 : -3 : 2


Substituting in (1),


4x – 3 (y + 1) + 2z = 0


4x – 3y + 2z – 3 = 0


Therefore equation of plane is 4x – 3y + 2z – 3 = 0

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