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Let A (2, 3 ,5), B (-1, 3, 2) and C $(\lambda ,5,\mu)$ be the vertices of a $\Delta$ ABC. 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)

best_answer

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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prateek

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