Math 210 Lecture 3: Lines, planes and
surfaces
Daniel Ingebretson
University of Illinois at Chicago
June 14, 2024
,Warmup: parametrizations of lines in R2
Graph the line y = 3 − x on the xy -plane.
,Warmup: parametrizations of lines in R2
Graph the line y = 3 − x on the xy -plane.
Graph the line with parametrization x(t) = 1 + t and
y (t) = 2 − t.
, Parametrizations as vector-valued functions
Let’s rewrite the parametrization x(t) = 1 + t and
y (t) = 2 − t as follows:
r(t) = ⟨x(t), y (t)⟩
surfaces
Daniel Ingebretson
University of Illinois at Chicago
June 14, 2024
,Warmup: parametrizations of lines in R2
Graph the line y = 3 − x on the xy -plane.
,Warmup: parametrizations of lines in R2
Graph the line y = 3 − x on the xy -plane.
Graph the line with parametrization x(t) = 1 + t and
y (t) = 2 − t.
, Parametrizations as vector-valued functions
Let’s rewrite the parametrization x(t) = 1 + t and
y (t) = 2 − t as follows:
r(t) = ⟨x(t), y (t)⟩
