Question

ABC is a triangle where $A=(2,3,5),B=(-1,2,2)$ and $C(\lambda ,5,\mu )$ if the median through A is equally inclined to the positive axis then $\lambda +\mu$ is

• A. 7
• B. 6
• C. 15
• D. 9

Answer 1

Answer: (C)

15

$AD$ is median $D\left(\frac{\lambda -1}{2},\frac{7}{2},\frac{\mu +2}{2}\right)$

$\overrightarrow{AD}=\left(\frac{\lambda -1}{2}-2,\frac{7}{2}-3,\frac{\mu +2}{2}-5\right)$

$\overrightarrow{AD}$ is equally in lined. $\therefore$paralle to $(1,1,1)$

$\begin{array}{c}\frac{\lambda -5}{2}=\frac{1}{2}=\frac{\mu +8}{2}\\ \lambda =6\\ \mu =9\\ \lambda +\mu =15\end{array}$

Then,

Option $C$ is correct answer.