ABC is triangle in a plane with vertices A(2, 3, 5), B (-1 , 3, 2… - Vidyadip

MCQ

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

A
$1130$
✓
$1348$
C
$1077$
D
$676$

✓

Answer

Correct option: B.

$1348$

b
$DR'$ of $AD$ are $\frac{{\lambda - 1}}{2}\,\, - 2,4 - 3,\frac{{\mu + 2}}{2}\, - 5$

i.e. $\frac{{\lambda - 5}}{2}\,\,,1,\frac{{\lambda - 8}}{2}\,\,$

$\because$ This median is making equal angles with coordinate axes, therefore,

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

$ \Rightarrow \lambda = 7\,\,\& \,\,\mu = 10$

$\therefore {\lambda ^3} + {\mu ^3} = 5 = 1348$

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