Maths-
General
Easy

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 lines. On the basis of the above information answer the following For f=g=h=1 both lines satisfy the relation

Hint:

## The correct answer is: All the above

### Given That:                   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 lines. On the basis of the above information answer the following For f=g=h=1 both lines satisfy the relational+bm+cn=0.....(1)⇒fmn+gln+hlm=0....(2)From (1)⇒n=−(al+bm)/cPutting in (2), we get⇒(fm+gl)[−(al+bm)/c]+hlm=0⇒ag(l/m)2+(af+bg−ch)l/m+bf=0....(1)if f=g=h=1∴a(l/m)2+(a+b−c)(l/m)+b=0From (1)⇒m=−(al+cn)/bPutting in (2), we getIf f=g=h=1c(nl)2+(c+a−b)n/l+a=0From (1)⇒l=−(cn+bm)/aPutting in (2), we getif f=g=h=1b(mn)2+(b+c−a)(m/n)+c=0>>> Therefore, all the given options are correct.

All the above options are correct.