Three Dimensional Geometry Question 392
Question: The foot of the perpendicular from the point (1, 6, 3) to the line $ \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} $ is
Options:
A) (1, 2, 5)
B) (-1, -1, 0)
C) (2, 5, 8)
D) (-2, -3, -4)
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Equation of line is $ \frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} $ Any point on this line is $ (K,2K+1,3K+2.) $ if this is the foot of perpendicular form (1, 6, 3) then d. r of this perpendicular are $ <K-1,2K-5,3K-1> $ Now, using condition of perpendicularly we have $ (K-1)1+(2K-5)2+(3K-1)3=0 $
$ \Rightarrow K-1+4K-10+9K-3=0\Rightarrow K=1 $ Hence, required foot of perpendicular is $ (1,3,5) $
BETA
