Let A (2, 3 ,5),  B (-1, 3, 2) and C  (\lambda ,5,\mu)  be the vertices of a \DeltaABC. If the median through A is equally inclined to the coordinate axes, then :

  • Option 1)

    5\lambda -8\mu =0

  • Option 2)

    8\lambda -5\mu =0

  • Option 3)

    10\lambda -7\mu =0

  • Option 4)

    7\lambda -10\mu =0

 

Answers (1)
P Prateek Shrivastava

As we learnt in

Direction Ratios -

(i)     if a,b,c are direction ratios then direction cosines will be

l=\frac{\pm a}{\sqrt{a^{2}+b^{2}+c^{2}}},m=\frac{\pm b}{\sqrt{a^{2}+b^{2}+c^{2}}}, n=\frac{\pm c}{\sqrt{a^{2}+b^{2}+c^{2}}}

(ii)        Direction ratios of line joining two given points

A\left ( x_{1},y_{1},z_{1} \right )\, and \, B\left ( x_{2},y_{2},z_{2} \right ) is given by

        \left ( x_{2}-x_{1},y_{2}-y_{1},z_{2}-z_{1} \right )

(iii)    If  r= a\hat{i}+b\hat{j}+c\hat{k} be a vector with direction cosines l, m, n then

l= \frac{a}{\left | r \right |},m= \frac{b}{\left | r \right |},n= \frac{c}{\left | r \right |}

-

 DRS of median = \left ( \frac{5-\lambda }{2}-1, \frac{8-\mu }{2} \right )

All are same,

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

\lambda =7, \mu = 10

Thus, 

10\lambda -7\mu =0


Option 1)

5\lambda -8\mu =0

This opttion is incorrect

Option 2)

8\lambda -5\mu =0

This opttion is incorrect

Option 3)

10\lambda -7\mu =0

This opttion is correct

Option 4)

7\lambda -10\mu =0

This opttion is incorrect

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