You say that L square +m square + n square =1 , where L, m, n are direction cosine, but in the question where they have given direction cosine , I cannot see any such thing,
Q. Find the direction cosine of the line which is perpendicular to the lines WITH DIRECTION COSINES PROPORTIONAL TO ;

Dear Student,
Please find below the solution to the asked query:

If l,m,n are direction cosines of a line then following property is always satisfied.l2+m2+n2=1In questions you are talking about, direction ratios not direction cosines would have been given.If l,m,n are direction cosines and a,b,c are direction ratios of the line then:la=mb=nc=cosnstantAlso if a,b,c are given then l,m,n are given by:l,m,n=aa2+b2+c2,ba2+b2+c2,ca2+b2+c2The question you have posted is incomplete. Please post the complete question alongwith dataso that we can help you better.

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