301 Abstract Algebra
2:00 - 2:50 MWF
Hentzel 432 Carver
hentzel@iastate.edu
Web Page   http://www.math.iastate.edu/hentzel/class.301

Text: A First Course in Abstract Algebra, sixth Edition
by John B. Fraleigh
Course: Chapter 1,2,3,4,5

Wednesday, December 12  

Main Idea:   
Key Words: 
Goal: 

            (1) rotate 60 degrees about the line { 1, 1, 1}.

            (2) rotate 60 degrees about the line {-1, 1,-1}.

            (3) rotate 60 degrees about the line { 1,-1,-1}.


(a) Give the final positions of the points {1,0,0},{0,1,0},{0,0,1}.

(b) Give the rotation and the axis to return everything back the


r1 =  {3,  1, 1,  1}

r2 =  {3, -1, 1, -1}

r3 =  {3,  1,-1, -1}




r2xr2xr1 = {32, 24, 8, -8}

Cos[1/2 theta] = 32/Sqrt[1728] =  4/(3 Sqrt[3])

theta = 79.3281 degrees.

The inverse is to rotate -79.3281 about the axis { 3,1,-1}


{1,0,0} --->  1/27 {23,  -2,-14};

{0,1,0} ----> 1/27 {14,  7,  22}; 

{0,0,1} ----> 1/27 {2, -26,   7};


r3xr2xr1 =   | 32             {-24, -8, 8}  |
             | {24, 8, -8}    32            |