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!

Homework Help: Linear Trans. Rotations

  1. May 6, 2007 #1
    Derive the matrix for the transformation that rotates a point (x,y,z) counterclockwise about the y-axis through an angle (X).

    My book gives me a matrice for the y-axis move.

    (cosX 0 sinX)
    (0 1 0 )
    (-sinX 0 cosX)

    call the above matrix [A]

    Im also given this formula for a unit vector

    cos(V)i + cos(W)j + cos(Y)k

    The way that I see the question, is that I need to somehow derive matix [A]
    from the given unit vector formula.

    I just dont see exactly how they are connected here.

    I really DON'T want the solution for this, just some insight maby on the connection between the formula and the matrix.

    I know that if I have a vector u and an angle (X) I can just multiply
    Au to get the rotated vector. So I do know how to use the matrix.
  2. jcsd
  3. May 6, 2007 #2
    The formula can be written as a matrix vector (cos(V) cos(W) cos(Y))^T.

    You are really looking for the linear transformation matrix such that L(x,y,z) rotates the standard basis for lR^3 by an angle X.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook