JEE MAIN - Mathematics (2016 - 10th April Morning Slot - No. 13)
ABC is a triangle in a plane with vertices
A(2, 3, 5), B(−1, 3, 2) and C($$\lambda $$, 5, $$\mu $$).
If the median through A is equally inclined to the coordinate axes, then the value of ($$\lambda $$3 + $$\mu $$3 + 5) is :
A(2, 3, 5), B(−1, 3, 2) and C($$\lambda $$, 5, $$\mu $$).
If the median through A is equally inclined to the coordinate axes, then the value of ($$\lambda $$3 + $$\mu $$3 + 5) is :
1130
1348
676
1077
Explanation
_10th_April_Morning_Slot_en_13_1.png)
DR's of AD are
$${{\lambda - 1} \over 2} - 2,{{5 + 3} \over 2} - 3,{{\mu + 2} \over 2} - 5$$
i.e. $${{\lambda - 5} \over 2},\,\,1,\,\,{{\mu - 8} \over 2}$$
As medium is making equal angles with coordinate axes,
$$ \therefore $$ $${{\lambda - 5} \over 2} = 1 = {{\mu - 8} \over 2}$$
$$ \Rightarrow $$ $$\lambda $$ = 7, $$\mu $$ = 10
$$ \therefore $$ $$\lambda $$3 + $$\mu $$3 + 5 = 73 + 103 + 5 = 1348
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