Correct Answer - Option 1 : x + 2y + 2z + 3 = 0
Concept:
The equation of a plane parallel to plane ax + by + cz + d = 0 is given by ax + by + cz + k = 0;
The distance of point p = (x1, y1, z1) from a plane ax + by + cz + d = 0 is given by
\(d = \frac{{\left| {a{x_1} + b{y_1} + c{z_1} + d} \right|}}{{\sqrt {{a^2} + {b^2} + {c^2}} }}\)
Calculation:
Given equation of a plane parallel to x + 2y + 2z = 5
⇒ equation of plane = x + 2y + 2z + k = 0;
Given unit distance from origin i.e. (0, 0, 0);
\( \Rightarrow 1 = \frac{{\left| k \right|}}{{\sqrt {{1^2} + {2^2} + {2^2}} }}\)
⇒ k = 3 or -3;
The final equation of plane will be
x + 2y + 2z + 3 = 0 or x + 2y + 2z -3 = 0
