Let the foot of perpendicular of the point P 3 , – 2 , – 9 on the plane passing through the points – 1 , – 2 , – 3 , 9 , 3 , 4 , 9 , – 2 , 1 be Q α , β , γ . Then the distance Q from the origin is

Step-by-step solution

Given that three points lie on a plane, A C → = 10 i ^ + 4 k ^ A B → = 10 i ^ + 5 j ^ + 7 k ^ A C → × A B → = i ^ j ^ k ^ 10 0 4 10 5 7 ⇒ A C → × A B → = - 20 i ^ - 30 j ^ + 50 k ^ ⇒ A C → × A B → = 2 i ^ + 3 j ^ - 5 k ^ Equation of plane will be, ⇒ 2 x + 3 y - 5 z = d And the plane passing through, – 1 ,   – 2 ,   – 3 ⇒ - 2 - 6 + 15 = d ⇒ d = 7 ∴   2 x + 3 y - 5 z = 7 Now finding the