Three Dimensional Geometry Question 5
Question: The point of intersection of the line passing through (0, 0, 1) and intersecting the lines $ x+2y+z=1 $ , $ -x+y-2z=2 $ and $ x+y=2,x+z=2 $ with xy plane is
Options:
A) $ ( \frac{5}{3},-\frac{1}{3},0 ) $
B) (1, 1, 0)
C) $ ( \frac{2}{3},-\frac{1}{3},0 ) $
D) $ ( -\frac{5}{3},\frac{1}{3},0 ) $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Equation of line. $ x+2y+z-1+\lambda (-x+y-2z-2)=0 $ …(i) $ x+y-2+\mu (x+z-2)=0 $ …(ii) (0, 0, 1) lies on it
$ \Rightarrow \lambda =0,\mu =-2 $ …(iii) For point of intersection, z=0 and solve (i) and (ii).
BETA
