If the length of the perpendicular drawn from the point P a , 4 , 2 , a > 0 on the line x + 1 2 = y - 3 3 = z - 1 - 1 is 2 6 units and Q α 1 , α 2 , α 3 is the image of the point P in this line, then a + ∑ i = 1 3 α i is equal to

Step-by-step solution

Let a point on the line x + 1 2 = y - 3 3 = z - 1 - 1 = λ be M 2 λ - 1 , 3 λ + 3 , - λ + 1 and the DR's of the line are 2 , 3 , - 1 The DR's of line joining the points 2 λ - 1 , 3 λ + 3 , - λ + 1 and a , 4 , 2 will be 2 λ - 1 - a , 3 λ - 1 , - λ - 1 Now its perpendicular to the given line, so 2 λ - 1 - a 2 + 3 λ - 1 3 + - λ - 1 - 1 = 0 ⇒ 4 λ - 2 - 2 a + 9 λ - 3 + λ + 1 = 0 ⇒ 14 λ - 4 - 2 a = 0 ⇒ 7 λ -