Thread: find a point in the plane

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.

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

Originally Posted by barriboy

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.

That's not "trickery", that is just using the equation of the plane. Of course, you probably won't be asked something that simple. You are more likely to be asked to find points in the plane that satisfy some other condition.

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.