Three Dimensional Geometry Question 47
Question: The length of the perpendicular drawn from (1, 2, 3) to the line $ \frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2} $ is
Options:
A) 4
B) 5
C) 6
D) 7
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Let P be the point (1, 2, 3) and PN be the length of the perpendicular form P on the given line. Coordinates of point N are $ (3\lambda +6,2\lambda +7,-2\lambda +7) $ . Now PN is perpendicular to the given line or vector $ 3\hat{i}+2\hat{j}-2\hat{k}. $ Thus, $ 3(3\lambda +6-1)+2(2\lambda +7-2)-2(-2\lambda +7-3)=0 $ Or $ \lambda =-1 $ Then, point N is (3, 5, 9)
$ \Rightarrow PN=7 $
BETA
