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Homework Help: Angle between line l and line m is 60degree

  1. May 28, 2012 #1
    1. The problem statement, all variables and given/known data
    The line l has the equation r= s(1,2,-1) and the line m has the equation r= (0,1,1)+t(5,a,5). Find the value of a such that the angle between the line l and m is 60degree.

    3. The attempt at a solution
    What I did was use the equation s(1,2,-1)xt(5,a,-5) = [tex]\sqrt{1^2 + 2^2 + 1^2}[/tex]x[tex]\sqrt{5^2 + a^2 + 5^2}[/tex] x cos 60
  2. jcsd
  3. May 28, 2012 #2


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    Yes, [itex]\vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta)[/itex].
    So [itex]\sqrt{6}\sqrt{50+ a^2}cos(60)= 10+ 2a[/itex]
    All you have to do is solve that equation for a. I recommend squaring both sides to get rid of the square root and solving the resulting quadratic equation.
    Last edited by a moderator: May 28, 2012
  4. May 28, 2012 #3

    Yea finally I am able to solve it. I was having dilemma on the square root part but your advice had been really helpful. Thanks a lot HallsofIvy. Cheers :smile:
    I got my answer a = [tex]\sqrt{30}[/tex]. I accidentally put s(1,2,-1)xt(5,a,-5) when its suppose to be s(1,2,-1)xt(5,a,5) therefore its suppose to be 2a instead of 10+2a.
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