Question

$ABC$ is a triangle in a plane with vertices $A(2,3,5),B(-1,3,2)$ and $C(\lambda ,5,\mu )$. If the median through A is equally inclined to the coordinate axes, then the value of $({\lambda }^3+{\mu }^3+5)$ is:

• A. $1130$
• B. $1348$
• C. $1077$
• D. $676$

Answer 1

Answer: (B)

$1348$

DR's of AD are $\frac{\lambda -1}{2}-2,4-2,\frac{\mu +2}{2}-5$
i.e. $\frac{\lambda -5}{2},1,\frac{\mu -8}{2}$
$\because$ This median is making equal angles with coordinate axes, therefore,
$\frac{\lambda -5}{2}=1=\frac{\mu -8}{2}$
$\Rightarrow \lambda =7$ and $\mu =10$
$\therefore {\lambda }^3+{\mu }^3+5=1348$