(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How to convert an implicit representation to a parametric

2. Relevant equations

Implicit: ax + by + cz = d.

Parametric: (x,y,z) = (xp, yp, zp) + s(xv,yv,zv,) + t(xw,yw,wz)

3. The attempt at a solution

For parametric to implicit it would look like this:

(x,y,z) = (0, 7, 6)T + s(-8, 7, -2)T + t(4, 1, -2)T

1. Calculate the crossproduct of (-8,7,-2) x (4,1,-2) = (12,24,36) = (1,2,3) = (a,b,c)

2. Calculate d using the first point: (1,2,3) (0,7,6) = d = 32

3. Result: 1x + 2y + 3z = 32

But how to go the other way around? I have looked all over google and youtube, but couldn't find it anywhere! :(.

Example could be: x + 2y + 3z = 32

I'm sorry that I couldn't try it before posting this. But I have no idea how to start :(.

Please help me.. my exam is on tuesday and I've been learning very hard.

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