If the point P ( α , β , γ ) lies on the plane 2 x + y + z = 1 and α β γ 1 9 1 8 2 1 7 3 1 = 0 0 0 , then α 2 + β 2 + γ 2 =

Step-by-step solution

Since, point P α , β , γ lies on the plane therefore, it satisfy the equation of plane and therefore we have 2 α + β + γ = 1     . . . i Now, we have, α β γ 1 9 1 8 2 1 7 3 1 = 0 0 0 ⇒ α + 8 β + 7 γ 9 α + 2 β + 3 γ α + β + γ = 0 0 0 Hence, α + 8 β + 7 γ = 0           . . . i i 9 α + 2 β + 3 γ = 0       . . . i i i α + β + γ = 0