    Question

# Suppose the direction cosines of two lines are given by al+bm+cn=0 and fmn+gln+hlm=0 where f,g,h,a,b,c are arbitrary constants and l,m,n are direction cosines of the line. On the basis of the above information and for f=g=h=1 both lines satisfy the relation:

A
a(lm)2+(a+bc)(lm)+b=0
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B
b(mn)2+(b+ca)(mn)+c=0
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C
c(nl)2+(c+ab)nl+a=0
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D
All of the above.
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Solution

## The correct option is D All of the above.al+bm+cn=0.....(1) ⇒fmn+gln+hlm=0....(2) From (1)⇒n=−(al+bmc) Putting in (2), we get ⇒(fm+gl)[−(al+bmc)]+hlm=0 ⇒ag(lm)2+(af+bg−ch)lm+bf=0....(1) if f=g=h=1 ∴a(lm)2+(a+b−c)(lm)+b=0 From (1)⇒m=−(al+cnb) Putting in (2), we get If f=g=h=1 c(nl)2+(c+a−b)nl+a=0 From (1)⇒l=−(cn+bma) Putting in (2), we get if f=g=h=1 b(mn)2+(b+c−a)(mn)+c=0  Suggest Corrections  0      Similar questions  Related Videos   Direction Cosines and Direction Ratios
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