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Home » has vertices at and . If the median through A is equally inclined to the axes, then the values of and respectively are (A) 10,7 (B) 9,10 (C) 7,9 (D) 7,10
\Delta A B C has vertices at A=(2,3,5), B=(-1,3,2) and C=(\lambda, 5, \mu). If the median through A is equally inclined to the axes, then the values of \lambda and \mu respectively are
(A) 10,7
(B) 9,10
(C) 7,9
(D) 7,10
maths | Maths
\Delta A B C has vertices at A=(2,3,5), B=(-1,3,2) and C=(\lambda, 5, \mu). If the median through A is equally inclined to the axes, then the values of \lambda and \mu respectively are
(A) 10,7
(B) 9,10
(C) 7,9
(D) 7,10

Correct option is

(D) 7,10

\begin{array}{l} \mathrm{D} \equiv\left(\frac{\lambda-1}{2}, \frac{5+3}{2}, \frac{\mu+2}{2}\right) \\ \equiv\left(\frac{\lambda-1}{2}, 4, \frac{\mu+2}{2}\right) \end{array}

Direction ratios of \mathrm{AD} are \frac{\lambda-1}{2}-2,4-3, \frac{\mu+2}{2}-5

i.e. \frac{\lambda-1-4}{2}, 1, \frac{\mu+2-10}{2}

i.e. \frac{\lambda-5}{2}, 1, \frac{\mu-8}{2}

Since the line \mathrm{AD} is equally inclined to coordinate axes, its direction ratios are in ratio \pm 1: \pm 1: \pm 1

\begin{array}{l} \therefore \frac{\frac{\lambda-5}{2}}{1}=\frac{1}{1} \\ \Longrightarrow \lambda-5=2 \\ \Longrightarrow \lambda=7 \end{array}

Also, \frac{1}{\frac{\mu-8}{2}}=\frac{1}{1}

\begin{array}{l} \Longrightarrow \frac{\mu-8}{2}=1 \\ \Longrightarrow \mu=10 \end{array}

Hence, the values of \lambda and \mu are 7 and 10 respectively.

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