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  • Need clarity, kindly explain! ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, µ). If the median through A is equally inclined to the coordinate axes, then the value of (λ3+µ3+5) is :

ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, µ).  If the median through A is equally inclined to the coordinate axes, then the value of (λ3+µ3+5) is :

  • Option 1)

    1130

  • Option 2)

     1348

  • Option 3)

    676

  • Option 4)

    1077

 

Answers (1)

As learnt in concept

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 )

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

\lambda=7;\mu=10

So, \lambda^{3}+\mu^{3}+5

=7^{3}+10^{3}+5=343+1000+5=1348


Option 1)

1130

This option is incorrect

Option 2)

 1348

This option is correct

Option 3)

676

This option is incorrect

Option 4)

1077

This option is incorrect

Posted by

Sabhrant Ambastha

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