Question

Let A (2, 3, 5), B (-1, 3, 2) and C($\lambda ,5,\mu$) be the vertices of a $\Delta$ ABC. If the median through A is equally inclined to the coordinate axes, then :

• A. $5\lambda -8\mu =0$
• B. $7\lambda -10\mu =0$
• C. $10\lambda -7\mu =0$
• D. $8\lambda -5\mu =0$

Answer 1

Answer: (C)

$10\lambda -7\mu =0$

Midpoint of B and C

$(\frac{\lambda -1}{2},4,\frac{\mu +2}{2})$

Now, D.R.'s of median will be

$(\frac{\lambda -1}{2}-2,4-3,\frac{\mu +2}{2}-5)$ .

$(\frac{\lambda -5}{2},1,\frac{\mu -8}{2})$

D.C.'s will be same since it is equally inclined to the coordinate axis.

$\frac{\lambda -5}{2}=1=\frac{\mu -8}{2}$

$\Rightarrow \lambda =7and\mu =10$

$\therefore \frac{\mu }{\lambda }=\frac{10}{7}$