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HOME-MADE HOMEWORK SUPPLEMENT MATH 2573H, FALL 2011
 

Summary: HOME-MADE HOMEWORK SUPPLEMENT
MATH 2573H, FALL 2011
UNIVERSITY OF MINNESOTA
GREG W. ANDERSON
Background
Suppose we are given two vectors v and w (in three-dimensional space) such that
|v| = |w| = 0, both with tails at the origin. There is a unique circle with center at
the origin passing through the heads of v and w. We would like to parameterize
that circle. The basic idea is to look at the vector
x =
v w
|v w|
v.
which is cooked up to have these properties:
|x| = |v| = |w|.
x v = 0.
w = cos()v + sin()x where 0 < < is the angle between v and w.
It turns out that the parametric formula
cos(t)v + sin(t)x for 0 t
describes a "great circle" trip from v to w. You can use this fact for the homework

  

Source: Anderson, Greg W. - School of Mathematics, University of Minnesota

 

Collections: Mathematics