Three-Dimensional-Geometry Question 423
Question: If x co-ordinates of a point P of line joining the points $ Q(2,,2,,1) $ and $ R,(5,,2,-2) $ is 4, then the z-coordinates of P is
[RPET 2000]
Options:
A) ? 2
B) ?1
C) 1
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
Suppose P divides QR in the ratio $ \lambda :1 $ . Then co-ordinates of P are $ ( \frac{5\lambda +2}{\lambda +1},,\frac{\lambda +2}{\lambda +1},,\frac{-2\lambda +1}{\lambda +1} ) $ . It is given that the x-coordinate of P is 4. i.e., $ \frac{5\lambda +2}{\lambda +1}=4 $ Þ $ \lambda =2 $ So, z-coordinate of P is $ \frac{-2\lambda +1}{\lambda +1}=\frac{-4+1}{2+1}=-1 $ .
BETA
