JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q83

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MathematicsSingle correct+4 / -1Question 83 of 90

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 :

5\lambda-8\mu=0

8\lambda-5\mu=0

10\lambda-7\mu=0

7\lambda-10\mu=0

Answer and worked solution

Official answer: C

The midpoint of BC is $\left(\frac{\lambda-1}2,4,\frac{\mu+2}2\right)$ . The median from A has direction $\left(\frac{\lambda-5}2,1,\frac{\mu-8}2\right)$ .

Equal inclination to the axes means equal direction ratios: $\lambda-5=2$ and $\mu-8=2$ . So $\lambda=7$ , $\mu=10$ , and $10\lambda-7\mu=0$ .

Topics:Direction cosines and ratios Distance and section formulae

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 83