Question

Which of the statement is true? The coordinate planes divide the line joining the points (4, 7, -2) and
(-5, 8, 3)

• A. all externally
• B. two externally and one internally
• C. two internally and one externally
• D. None of the above

Answer 1

The correct option is C two internally and one externally

If ratio $\lambda :1$, then points divide (4, 7, -2) and (-5, 8, 3) is
$(\frac{4-5\lambda }{\lambda +1},\frac{7+8\lambda }{\lambda +1},\frac{-2+3\lambda }{\lambda +1})$
For XOY plane$z=0,\frac{-2+3\lambda }{\lambda +1}=0$
$\Rightarrow \frac{\lambda }{1}=\frac{2}{3},\lambda :1=2:3$ (internally)
For YOZ plane $x=0,\frac{4-5\lambda }{\lambda +1}=0$
$\Rightarrow \lambda =\frac{4}{5},\lambda :1=4:5$ (internally)
and for ZOX plane $y=0,\frac{7+8\lambda }{\lambda +1}=0$
$\Rightarrow \lambda =-\frac{7}{8},\lambda :1=-7:8$ (externally)
ie, two internally and one externally.