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
- 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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