An angle between the  lines whose direction cosines are given by the equation l+3m+5n=0 and· 5lm−2mn+6nl=0, is

An angle between the  lines whose direction cosines are given by the equation l+3m+5n=0 and· 5lm2mn+6nl=0, is

  1. A

    cos1(1/8)

  2. B

    cos1(1/3)

  3. C

    cos1(1/4)

  4. D

    cos1(1/6)

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    Solution:

    The given equations are 

    l+3m+5n=0                                 …(i)

    5lm2mn+6nl=0                         …(ii)   

    From (i) l=3m5n

    Putting this value of I in (ii), we have 

    5(3m5m)m2mn+6n(3m5n)=0

    15m230n245mn=0m2+2n2+3mn=0m2+3mn+2n2=0m(m+2n)+n(m+2n)=0

     (m+n)(m+2n)=0either m=n or m=2n

    For, m=n,l=2n; for ;m=2n,l=n

     Direction ratios of two lines are 

    2n,n,n and n,2n,n

    i.e. 2,1,1 and 1,2,1

     The required angle is

    cosθ=21+21+114+1+11+4+1 cosθ=166=16θ=cos116

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