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

  1. a open parentheses 1 over m close parentheses squared plus left parenthesis a plus b minus c right parenthesis open parentheses 1 over m close parentheses plus b equals 0
  2. b open parentheses m over n close parentheses squared plus left parenthesis b plus c minus a right parenthesis open parentheses m over n close parentheses plus c equals 0
  3. c open parentheses n over l close parentheses plus left parenthesis c plus a minus b right parenthesis n over 1 plus a equals 0
  4. All the above

hintHint:

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+bgch)l/m+bf=0....(1)
    if f=g=h=1
    a(l/m)2+(a+bc)(l/m)+b=0

    From (1)m=(al+cn)/b
    Putting in (2), we get
    If f=g=h=1
    c(nl)2+(c+ab)n/l+a=0

    From (1)l=(cn+bm)/a
    Putting in (2), we get
    if f=g=h=1
    b(mn)2+(b+ca)(m/n)+c=0
    >>> Therefore, all the given options are correct.

    All the above options are correct.

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