ABC is a triangle in a plane with vertices A(2,3,5), B(-1,3,2) and C(,5,).

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:

Accepted Answer

DR's of AD are

$${{\lambda  - 1} \over 2} - 2,{{5 + 3} \over 2} - 3,{{\mu  + 2} \over 2} - 5$$

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

As medium is making equal angles with coordinate axes,

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

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

$$ \therefore $$   $$\lambda $$3 + $$\mu $$3 + 5 = 73 + 103 + 5 = 1348

Solutions · 1