Let the system of linear equations – x + 2 y - 9 z = 7 - x + 3 y + 7 z = 9 - 2 x + y + 5 z = 8 - 3 x + y + 13 z = λ has a unique solution x = α , y = β , z = γ . Then the distance of the point α , β , γ from the plane 2 x - 2 y + z = λ is

Step-by-step solution

Given, System of linear equation, – x + 2 y - 9 z = 7   . . . . . . . i – x + 3 y + 7 z = 9   . . . . . . . ii – 2 x + y + 5 z = 8   . . . . . . iii – 3 x + y + 13 z = λ   . . . . . . iv Now solving, equations i ,   ii   &   iii we get, x = – 3 ,   y = 2 ,   z = 0 Now substituting in equation iv we get, 3 × 3 + 2 = λ ⇒ λ = 11 Now finding the distance of Point – 3 ,   2 ,   0 from the plane 2 x -