Let S be the mirror image of the point Q ( 1 , 3 , 4 ) with respect to the plane 2 x - y + z + 3 = 0 and let R ( 3 , 5 , γ ) be a point of this plane. Then the square of the length of the line segment S R is

Step-by-step solution

Let point S ( α , β , γ )   be   an   image   of   Q ( 1 , 3 , 4 ) then α - 1 2 = β - 3 - 1 = γ - 4 1 = - 2 ( 2 - 3 + 4 + 3 ) 4 + 1 + 1 = - 2 ⇒ S ( α , β , γ ) = ( - 3 , 5 , 2 ) and point R ( 3 , 5 , γ ) lies on the plane 2 x - y + z + 3 = 0 put the points of R in equation of plane anf find the value ⇒ 6 − 5 + γ + 3 = 0 ⇒ γ = − 4 ⇒ R ( 3 , 5 , − 4 ) & S ( − 3 , 5 , 2 ) using dista