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This belongs to Dc's and dr's
if the dc's of two lines are connected by relations l +m-n =0
6ln -12lm+ mn =0 then dc's of two line are.....?
(1/root14,2/root14,3/root14) , (1/root26,3/root26,4/root26)

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Solution

The answer is option A
(1/root14,2/root14,3/root14)
Given below is the steps to solve this problem.
At first consider the fact that there are 3 unknowns and only 2 equations are given.
But we know the general property of direction cosines.
They are governed by the equation;
l²+m²+n²=1
Now we have 3 equations and 3 unknowns.
Now write l in terms of m and n, this will reduce the number of variables to two.
Substitute this in second equation.
Now you will get 2 equation and 2 unknowns.
Substitute this in third equation to get the final third degree equation.
Solving this will give the above mentioned result.
Thank you

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