How to convert cartesian equations into vector or parametric equations?

• Dec 2nd 2008, 04:57 AM
JoeyCC
How to convert cartesian equations into vector or parametric equations?
Ok I am having difficulties converting cartesian into equations to parametric/vector equations.

By using the example provided could someone show me how it's done?
http://img34.picoodle.com/img/img34/...em_dedc78f.jpg
• Dec 2nd 2008, 10:20 AM
running-gag
Let A(1,5) and u(3,2)
M(x,y) is on the line passing through A with direction u means that exists k real such as AM = k u
Coordinates give the system
x - 1 = 3k
y - 5 = 2k

Parametric equation of the line is the system
x = 3k + 1
y = 2k + 5

To get the cartesian equation you have to eliminate k
2x = 6k + 2
3y = 6k + 15

Difference gives 2x - 3y = -13
A cartesian equation is therefore 2x - 3y + 13 = 0
• Dec 2nd 2008, 10:48 AM
Soroban
Hello, JoeyCC!

I believe the vector is: . $\vec v \;=\;(1+3t)\vec i + (5 + 2t)]\vec j$

• Dec 2nd 2008, 10:54 AM
JoeyCC
Thanks Man!