Q. The image of the point (3, -1, 11) in the line $\frac{x}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ is

2826 188 Three Dimensional Geometry Report Error

A

(1, 11, 3)

22%

B

(11, 11, 3)

13%

C

(3, 1, 11)

45%

D

(1, 3, 11)

20%

Solution:

Any point on the given line is (2t, 2 + 3t, 3 + 4t) .
it is the foot of perpendicular from (3, -1, 11)
if $(2 t - 3) \times 2 + (2 + 3 t + 1) \times 3 + (3 + 4 t - 11) \times 4 = 0$
$\Rightarrow t = 1$
So, the coordinates of foot of perpendicular are (2, 5, 7)
Now, the point (a, b, c) will be the image of the point (3, -1, 11) in the given line if
$\frac{3 + a}{2} = 2, \frac{b - 1}{2} = 5;$
$\frac{c + 11}{2} = 7 \Rightarrow a = 1, b = 11, c = 3$