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  • Let ABC be a triangle with vertices at points <img alt="A ( 2,\; 3,\; 5 ),\; B ( -1,\; 3,\; 2 )" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cinline%20A%20%28%202%2C%5C%3B%203%2C%5C%

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

Option: 1

(10,\; 7 )         


Option: 2

( 7,\;5 )


Option: 3

( 7,\; 10 )


Option: 4

( 5,\; 7 )


Answers (1)

best_answer

D is the midpoint of the line segment BC

\mathrm{D=\left(\frac{\lambda-1}{2}, 4, \frac{\mu+2}{2}\right)}

AD is the median of triangle ABC

Let the Direction ratio of AD be (a, b, c)

\\a=\left(\frac{\lambda-1}{2}-2\right)=\frac{\lambda-5}{2} ,\; b=4-3=1, \;c=\frac{\mu+2}{2}-5=\frac{\mu-8}{2}

\begin{aligned} &\text { for equal inclination all these should equal }\\ &\frac{\lambda-5}{2}=1=\frac{\mu-8}{2}\\ &\lambda=\mathbf{7}, \mathbf{\mu}=\mathbf{1 0} \end{aligned}

Posted by

Sanket Gandhi

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