describe these two reflections..
I can show this in the plane, but need to show it for 3 space..
2006-12-19 05:32:59 · 5 answers · asked by JAC 3 in Science & Mathematics ➔ Mathematics
Rotations in three space have an axis that is fixed. Imagine a plane perpendicular to that axis. Since you know how to do the two dimensional version, you have two reflections across lines in that plane. Extend these reflection to three dimensions by reflecting through a plane that contains the axis and the lines of reflection in the perpendicular plane.
2006-12-19 05:38:29 · answer #1 · answered by mathematician 7 · 3⤊ 1⤋
show that the general matrix of the rotation is a linear combination of 2 reflection matrices.
2006-12-19 13:47:33 · answer #2 · answered by ronald t 2 · 1⤊ 0⤋
Suppose you rotate the point (r,0) 180 degress to th point (-r,0).
Then only one reflection across the y-axis is needed to produce the rotation. This counterexample shows your hypothesis is not true for every case.
2006-12-19 13:59:30 · answer #3 · answered by ironduke8159 7 · 0⤊ 1⤋
As angular speed is a vector then it could be considered as a composition of two or more vectors; no special proof is necessary!
2006-12-19 16:21:33 · answer #4 · answered by Anonymous · 0⤊ 1⤋
Try multiplying out the 3 x 3 matrices.. that's why matrix multiplication is defined the way it is.
2006-12-19 13:38:18 · answer #5 · answered by Joni DaNerd 6 · 0⤊ 2⤋