Vector Rotations in 3D

vector start point

vector end point

rotation X

rotation Y

rotation Z

ϕ start

0.55

θ start

3.64

rotation

0.

This Demonstration lets you locate two points on a sphere. The points form a vector that can be rotated about the

X

,

Y

, or

Z

axes. The trace of the rotation is made using multiple vectors at 5° increments. Each of these vectors is the product of a rotation matrix (see Details) and the original vector.

Details

J. Stewart, Calculus, 5th ed., Belmont, CA: Brooks/Cole, 2003 pp. 840–842.

Rotation about the

X

axis by

γ

:

1	0	0
0	cosγ	-sinγ
0	sinγ	cosγ

;

rotation aboput the

Y

axis by

γ

:

cosγ	0	sinγ
0	1	0
-sinγ	0	cosγ

;

rotation about the

Z

axis by

γ

:

cosγ	-sinγ	0
sinγ	cosγ	0
0	0	1

.

External Links

Rotation Matrix (Wolfram MathWorld)

Permanent Citation

Stephen Wilkerson

"Vector Rotations in 3D"
http://demonstrations.wolfram.com/VectorRotationsIn3D/
Wolfram Demonstrations Project
Published: March 7, 2011