Maths-

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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

- All the above

Hint:

### Derive the directional cosines and find the relation between them.

## 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 relation

al+bm+cn=0.....(1)

⇒fmn+gln+hlm=0....(2)

From (1)⇒n=−(al+bm)/c

Putting 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=0

From (1)⇒m=−(al+cn)/b

Putting in (2), we get

If f=g=h=1

c(nl)^{2}+(c+a−b)n/l+a=0

From (1)⇒l=−(cn+bm)/a

Putting in (2), we get

if f=g=h=1

b(mn)^{2}+(b+c−a)(m/n)+c=0

>>> Therefore, all the given options are correct.

All the above options are correct.

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