Three Dimensional Geometry Question 168
Question: The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point $ ( 0,\frac{17}{2},\frac{-13}{2} ) $ . Then
Options:
A) $ a=2,,b=8 $
B) $ a=4,b=6 $
C) $ a=6,b=4 $
D) $ a=8,b=2 $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Equation of line through $ (5,1,\alpha ) $ and $ (3,b,1) $ is $ \frac{x-5}{-2}=\frac{y-1}{b-1}=\frac{z-a}{1-a}=\lambda $
$ \therefore $ Any point on this line is a $ [-2\lambda +5,(b-1)\lambda +1,(1-a)\lambda +a] $ It crosses yz plane where $ -2\lambda 5=0 $ $ \lambda =\frac{5}{2} $
$ \therefore ( 0,(b-1)\frac{5}{2}+1,(1-a)\frac{5}{2}+a )=( 0,\frac{17}{2}.\frac{-13}{2} ) $
$ \Rightarrow (b-1)\frac{5}{2}+1=\frac{17}{2} $ and $ (1-a)\frac{5}{2}+a=-\frac{13}{2} $
$ \Rightarrow b=4anda=6 $
BETA
