Question

The foot of the perpendicular from (0, 2,3) to the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ is:

• A. (–2, 3, 4)
• B. (2, –1, 3)
• C. (2, 3, –1)
• D. (3, 2, –1)

Answer 1

The correct option is C (2, 3, –1)

Any point on the given line is (5r – 3, 2r + 1, 3r – 4). If it is the foot of the perpendicular from (0, 2, 3), then 5(5r – 3 – 0) + 2(2r + 1 – 2) + 3(3r – 4 – 3) = 0
i.e.,38r = 38
i.e., r = 1
Foot of perpendicular is (2, 3, –1)