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Find parametric question for the plane 
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#1
May1707, 12:35 PM

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1. The problem statement, all variables and given/known data
Give parametric questions for the plane : 2x3y+z6=0 3. The attempt at a solution i know that the normal is (2,3,1) how do i find the direction vector of the plane? 


#2
May1707, 02:59 PM

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The plane has two linearly independent 'direction vectors'. Find any two independent vectors perpendicular to your normal.



#3
May1807, 07:44 AM

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Dick is assuming that by 'direction vector', you mean two independent vectors in the plane. I've only seen the term used with lines.
I wonder if you are not confusing this with "find the parametric equations for a line". To do that you would find 'direction vector' for the line. Parametric equations for a plane will involve two parameters. Here, since you can write z as a function of x and y, z= 6 2x+ 3y, you can use x and y themselves as parameters or, if you prefer distinct variables, x= u, y= w, z= 6 2u+3w. 


#4
May1807, 07:48 AM

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Find parametric question for the plane
That's a much more direct way. I was fixated on the 'direction vector' (basis) picture.



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