If the image of the point 1 , - 2 , 3 in the plane 2 x + 3 y - z = 7 is the point α , β , γ , then the value of α + β + γ is equal to

Step-by-step solution

Since, α ,   β ,   γ   is the image of the point 1 , - 2 ,   3 in the plane. So, we have, ∵ Image of  ( x 1 , y 1 , z 1 )  in the plane  a x + b y + c z + d = 0   is   given   by x − x 1 a = y − y 1 b = z − z 1 c = − 2 ( a x 1 + b y 1 + c z 1 ) a 2 + b 2 + c 2 α - 1 2 = β + 2 3 = γ - 3 - 1 = - 2 2 1 + 3 - 2 - 3 - 7 2 2 + 3 2 + - 1 2 ⇒ α - 1 2 = β + 2 3 = γ - 3 - 1 = -