Three Dimensional Geometry · Question 52

If the image of the point (4, 4, 3) in the line x - 12 = y - 21 = z - 13 is ( , , ), then + + is equal to

1. 12
2. 9
3. 7
4. 8

Answer

(2) 9

Solution

Any point on the line: F = (1 + 2 , 2 + , 1 + 3 )

PF = (2 - 3, - 2, 3 - 2), where P = (4, 4, 3)

F is the foot of the perpendicular PF (2, 1, 3) = 0

2(2 - 3) + ( - 2) + 3(3 - 2) = 0 14 - 14 = 0 = 1

F = (3, 3, 4)

F is the mid-point of P and its image:

( , , ) = 2F - P = (2, 2, 5)

+ + = 9

Answer: (2)