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There are many different measures of how well a plane fits given data, and different measures give rise to different best fitting planes So you had best tell us what you have in mind as your measure of how well a given plane fits some given data. 0 you do not have enough information to specify the exact value of d in your equation I would leave the equation as$$ x+11y+3z+d=0$$ until a point on the plane is given
At this point we have a family of parallel planes. Can you please explain to me how to get from a nonparametric equation of a plane like this $$ x_1−2x_2+3x_3=6$$ to a parametric one The equation of a plane that goes through the origin can be written as $ax+by+cz=0$
Method 1 gives you the direction of a line in your original plane There is no reason why this direction should be orthogonal to the plane you require Method 2 will work though as you now have 2 directions in the plane you have to find. Here's what i have so far:
I see that the related problem has a point on the plane supplied as well I think my main issue here is, how do i determine a point on the plane Can i use the origin (0,0,0) as a point on the plane, or can i simply use one of the vectors as a point on the plane?
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