Question

having trouble understanding how to sketch a plane curve represented by a vector valued function. ex: r(t)=t^2i+tj

Answer 1

r is the distance from the origin; as defined by the i and j components

Answer 2

or simply put r = <t^2,t>

Answer 3

x = t^2

y = t

+- sqrt(x) = t

y = +-sqrt(x)

Answer 4

http://www.wolframalpha.com/input/?i=y+%3D+-sqrt%28x%29+and+y%3Dsqrt%28x%29

Answer 5

so you always just convert it into x and y coordinates and graph it like normal?

Answer 6

r(0) = (0,0)
r(1) = (1,1)
r(2) = (4,2)
r(3) = (9,3)

Answer 7

well, yes and no :) depends on the relation between x and y

Answer 8

in this case; x is a function of t and y is a function of t so there is some relation between the 2

Answer 9

and it looks like it creates: y = sqrt(x)

Answer 10

so then should i be able to do this as long as x and y are both functions of t?

Answer 11

yes

Answer 12

ok, well it looks like that is all i will deal with for now so i guess that makes better sense. i just get caught off gaurd when i see another variable.

Answer 13

thank you!

Answer 14

your welcome