Question

XOZ -plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio

• A. 3 : 7
• B. 2 : 7
• C. -3 : 7
• D. -2 : 7

Answer 1

The correct option is C

-3 : 7

Let A = (2, 3, 1) and B = (6, 7, 1)

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

ratio $\lambda$:1.

Then, we have,

P$\equiv$ $(\frac{6\lambda +2}{\lambda +1},\frac{7\lambda +3}{\lambda +1},\frac{\lambda +1}{\lambda +1})$

Since P lies on the xz-plane, the y-coordinate of P will be zero.

$\therefore \frac{7\lambda +3}{\lambda +1}=0$

$\Rightarrow 7\lambda +3=0$

$\Rightarrow \lambda =\frac{-3}{7}$