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
