# Linear Trans. Rotations

1. May 6, 2007

### robierob12

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. May 6, 2007

### Mindscrape

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.