Let abc be a triangle with vertices at points a(2 3 5)

Let ABC be a triangle with vertices at points

Question:

Let $\mathrm{ABC}$ be a triangle with vertices at points $\mathrm{A}(2,3,5), \mathrm{B}(-1,3,2)$ and $\mathrm{C}(\lambda, 5, \mu)$ in three dimensional space. If the median through $\mathrm{A}$ is equally inclined with the axes, then $(\lambda, \mu$.) is equal to:

1. (10,7)$

2. $(7.5)$

3. $(7,10)$

4. $(5,7)$

Correct Option: , 3

Solution:

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Solution:

Since $AD$ is the median
∴D=(2λ−1​,4,2μ+2​) Now, dR’s of AD is

a=(2λ−1​−2)=2λ−5​

b=4−3=1,c=2μ+2​−5=2μ−8​ Also, a, b, c are dR’s

$\therefore a=kl,b=km,c=kn$ where $I=m=n$

and l2+m2+n2=1
⇒l=m=n=3​1​
Now, $a=1,b=1$ and $c=1$
$\Rightarrow \lambda =7and\mu =10$

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