1. Limited time only! Sign up for a free 30min personal 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!

Angles in 3d

  1. Jan 4, 2012 #1
    Hi guys,

    Wondering if you could help me on this one. If you have a vector in xyz, and you know the angles that the vector is inclined at to two of the axis, how do you find the 3rd one.

    eg, line inclined at 60˚ to the x axis and 45˚ to the y axis, how do you find the inclination to the z axis (which is 60˚ or 120˚ by the way) I know it has something to do with direction ratios and direction cosines, but don't know how to get there. I also know that direction cosines add up to 1, but I can't find a connection.

    Thanks in advance

    Rob
     
  2. jcsd
  3. Jan 4, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Use "direction cosines". If [itex]\theta[/itex], [itex]\phi[/itex], and [itex]\psi[/itex] are the angles a direction makes with the x, y, and z axes respectively, then [itex]cos(\theta)\vec{i}+ cos(\phi)\vec{j}+ cos(\psi)\vec{k}[/itex] is the unit vector in that direction.

    That means that if you are given a vector, v, you can find the angles it makes with the axes by reducing it to a unit vector- divide by its length- and look at the components.

    In your example, you know that a unit vector in your direction is [itex]<cos(60), cos(45), cos(\psi)>= < 0.5, 0.707, cos(\psi)>[/itex] so you must have [itex].25+ 0.5+ cos^2(\psi) = 1[/itex]. You can solve that for [itex]\psi[/itex].
     
  4. Jan 4, 2012 #3
    Yes of course, that is so simple when it is explained. Thank you very much Hallsofivy.

    Happy new year.

    Rob K
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Angles in 3d
  1. 3d angles problem (Replies: 2)

Loading...