# Thread: Finding points and vectors in a plane.

1. ## Finding points and vectors in a plane.

3x+6y+9z=9 Find the coordinates of three points P, Q, and R in the plane, and determine the vectors PQ & PR?

I believe I have to solve this problem using the Standard Equation of a Plane in Space, but backwards. Honestly I don't know where to start, except maybe by dividing both sides of the equation by 3? Any assistance greatly appreciated.

2. ## Re: Vectors

Originally Posted by bagshotrow
3x+6y+9z=9 Find the coordinates of three points P, Q, and R in the plane, and determine the vectors PQ & PR?

I believe I have to solve this problem using the Standard Equation of a Plane in Space, but backwards. Honestly I don't know where to start, except maybe by dividing both sides of the equation by 3? Any assistance greatly appreciated.
Can't you find values of x, y and z that satisfy the equation (those values give you the coordinates of points in the plane)? eg. If x = 1 and y = 1 then it follows that z = 0. So (1, 1, 0) is a point in the plane. Call it P. etc.

Once you have three points P, Q and R, you should have been taught how to find vectors PQ and PR. Go back to your class notes and review that material.

If you need more help, please show all your work and say where you get stuck.

3. ## Re: Vectors

Sadly I have no notes, and this subject is not directly addressed in the book I am working out of. I have the Standard Equation of a Plane in Space Theorem, and the Parametric Equations of a Line in Space Theorem ans I guess I am suppose to figure the rest out somehow. I was thinking of the point (3,0,0) or (0,0,1) or (-1,2,0) but I believe there is more to it then just finding numbers to satisfy the equation. Thanks for you help and I will continue to try and fill in the blanks the book so kindly left me.

4. ## Re: Vectors

Originally Posted by bagshotrow
Sadly I have no notes, and this subject is not directly addressed in the book I am working out of. I have the Standard Equation of a Plane in Space Theorem, and the Parametric Equations of a Line in Space Theorem ans I guess I am suppose to figure the rest out somehow. I was thinking of the point (3,0,0) or (0,0,1) or (-1,2,0) but I believe there is more to it then just finding numbers to satisfy the equation.
That is all there is to it.
You have found three points on that plane.
Because there are finitely many such triples, there are multiple solutions the question.
NAME those points $\displaystyle P,~Q,~\&~R$.
Find $\displaystyle \overrightarrow {PQ} \;\& \,\overrightarrow {PR}$

5. ## Re: Vectors

Guess I was trying to over think the problem. Found my 3 points, found PQ and PR and found PQ x PR. Thanks you for your help Plato and Thank you Mr Fantastic for the nudge in the right direction. Usually all I need is that push in the right direction to get started and finish the problem. Good Night