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1. Lines and planes in Rn Definition 1.1. We say a subset L of Rn
 

Summary: 1. Lines and planes in Rn
.
Definition 1.1. We say a subset L of Rn
is a line if there are r0, v Rn
such that
v = 0 and
L = {r(t) : t R}
where we have set
(1) r(t) = r0 + tv for t R.
Remark 1.1. Thus
r : R Rn
and
rng r = L.
The function r is called a parameterization of L. It is obviously univalent; this
means that
t1, t2 R and r(t1) = r(t2) t1 = t2.
Theorem 1.1. Suppose
(i) L is a line in Rn
;
(ii) a, b L and a = b;

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics