# Three lines have direction ratios -1, -2, 2 ; 8, -1, 4 and 1, 4, 8. Find the direction ratios of a line which is equally inclined to them.

Arun Kumar IIT Delhi
8 years ago
$\lambda_{1},\lambda_{2},\lambda_{3} \\-\lambda_{1}-2\lambda_{2}+2\lambda_{3}=\lambda \\8\lambda_{1}-1\lambda_{2}+4\lambda_{3}=\lambda \\\lambda_{1}+4\lambda_{2}+8\lambda_{3}=\lambda$

Now try to understand the method of matrix.
$\lambda_{1}:\lambda_{2}:\lambda_{3}=\begin{pmatrix} 1 & -2 &2 \\ 1& -1& 4\\ 1& 4&8 \end{pmatrix}:\begin{pmatrix} -1 &1 & 2\\ 8& 1 &4 \\ 1& 1 &8 \end{pmatrix}:\begin{pmatrix} -1 &-2 &1 \\ 8& -1& 1\\ 1&4 &1 \end{pmatrix}$

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Arun Kumar
IIT Delhi