# Thread: How to convert cartesian equations into vector or parametric equations?

1. ## 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?

2. 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

3. Hello, JoeyCC!

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

4. Thanks Man!

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# how to change the cartesian equation 2x=3y=5z into vector form/mathematics 12

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