that is a perfectly valid and efficient choice to make, you could let
x= sqrt(17) y = e^2 and solve for z but that wouldn't be very efficient.
sometimes even math is as easy as it seems
we are just learning vectors, but need to find a point in a given plane. i have been trying to find a way to solve this for hours.
if given the eqn of the plane: x-3y -2z = 7
find a point p on the plane and a normal vector n to the plane.
i know that the normal must be <1, -3, -2>
but how am i supposed to find a point in the plane. I suppose you could try just make y and z 0 and then make x 7 to get a possible solution, but is there some rule that prevents this?
in any case, given that the entire question is finding a point, i think if i pulled some trickery like that, I will get no credit.
For example, "Find the point at which the line, given by x= 2t- 1, y= t+ 3, z= t- 4, intersects the plane, x-3y -2z = 7".
To do that, replace x, y, and z in the plane by those equations and solve for t.