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

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