1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the direction vector with only direction angles

  1. Nov 2, 2005 #1
    Hey everybody! Thanks for any help!

    If I am told a line has direction angles of 60, 45 and 60 and passes through the point (-2, 1, 3). How would I go about figuring out the symmetric equations of the line..

    Relatively simple question but I am a tad confused. HELP!
  2. jcsd
  3. Nov 3, 2005 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    If [tex]\theta[/tex], [tex]\phi[/tex], and [tex]\psi[/tex] are the "direction angles", then [tex]cos(\theta)[/tex], [tex]cos(\phi)[/tex], and [tex]cos(\psi)[/tex], the "direction cosines", form a unit vector in that direction.
    cos(60)= 1/2, cos(45)= [tex]\frac{\sqrt{2}}{2}[/tex] so a unit vector in the direction with direction angles 60, 45, 60 (degrees- it would be good idea to say that explicitely!) is [tex]\frac{1}{2}i+ \frac{\sqrt{2}}{2}j+ \frac{1}{2}k[/tex] and parametric equations for a line in that direction, passing through (-2, 1, 3) would be [tex]x= \frac{1}{2}t- 2[/tex], [tex]y= \frac{\sqrt{2}}{2}t+ 2[/tex], [tex]z= \frac{1}{2}t+ 3[/tex].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Finding the direction vector with only direction angles
  1. Direction Vector (Replies: 5)

  2. Direction vector (Replies: 3)