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:
(10,7)$
$(7.5)$
$(7,10)$
$(5,7)$
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
∴a=kl,b=km,c=kn where I=m=n
and l2+m2+n2=1
⇒l=m=n=31
Now, a=1,b=1 and c=1
⇒λ=7andμ=10
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