Question

The ratio in which the line joining the points $(a,b,c)$ and $(-a,-c,-b)$ is divided by the xy-plane is

• A. a : b
• B. b : c
• C. c : a

Answer 1

The correct option is C

c : a

Let A =(a, b, c) and B = (-a, -c, -c)

Let the line joining A and B be divided by the yz-plane at point P in the

ratio $\lambda :1$

Then, we have,

P = $(\frac{-a\lambda +a}{\lambda +1},\frac{-c\lambda +b}{\lambda +1},\frac{-b\lambda +c}{\lambda +1})$

Since P lies on the xy-plane, the z-coordinate of P will be zero.

$\therefore \frac{b\lambda +c}{\lambda +1}=0$

$\Rightarrow -b\lambda +c=0$

$\lambda =\frac{c}{b}$

Hence, the xz-plane divides AB in the ratio c : b