# Thread: Working out if points belong to a plane or not

1. ## Working out if points belong to a plane or not

Hello I came up this problem revising for my exam. I need help understanding some of the theory behind this...so if anyone can help I would extremely appreciate it.

u = i - 2j v = 2i + 3j

1. Find a Cartesian equation for the plane P containing the point Q(3,2,1) and parallel to u and v.

The plane will have the same normal as u and v. This means the normal is parallel to (0,0,1) making the formula for the plane be z = 1

Is this right?

2. Find the perpendicular distance between the plane P and the origin O (0,0,0)

For this the answer is (0,0,1) apparently. Could somebody explain me why it is this??

3. Which of the points A(1,2,2), B (2,1,1), C(-1,6,2) belong to the plane P?

How do I find this? Do I multiply the position vectors by the normal (0,0,1) and see if this is equal to 1?

Also does anybody know a good website explaining these type of problems because my notes and books do not cover it yet it is still in the exam!

Thanks for helping!

2. Originally Posted by gva0324 Hello I came up this problem revising for my exam. I need help understanding some of the theory behind this...so if anyone can help I would extremely appreciate it.

u = i - 2j v = 2i + 3j

1. Find a Cartesian equation for the plane P containing the point Q(3,2,1) and parallel to u and v.

The plane will have the same normal as u and v. This means the normal is parallel to (0,0,1) making the formula for the plane be z = 1

Is this right?

2. Find the perpendicular distance between the plane P and the origin O (0,0,0)

For this the answer is (0,0,1) apparently. Could somebody explain me why it is this??

3. Which of the points A(1,2,2), B (2,1,1), C(-1,6,2) belong to the plane P?

How do I find this? Do I multiply the position vectors by the normal (0,0,1) and see if this is equal to 1?

Also does anybody know a good website explaining these type of problems because my notes and books do not cover it yet it is still in the exam!

Thanks for helping!
Yes, the equation of the plane is z = 1. The perpendicular distance of the plane from the origin is obviously 1 - draw a diagram to see it. And while you're looking at your diagram, use it to see why it's obvious that points A and C cannot possibly lie in the plane z = 1(or just contemplate the equation z = 1 for a moment ....)

3. Originally Posted by gva0324 Hello I came up this problem revising for my exam. I need help understanding some of the theory behind this...so if anyone can help I would extremely appreciate it.

u = i - 2j v = 2i + 3j

1. Find a Cartesian equation for the plane P containing the point Q(3,2,1) and parallel to u and v.

The plane will have the same normal as u and v. This means the normal is parallel to (0,0,1) making the formula for the plane be z = 1

Is this right?
Yes, that is correct.

2. Find the perpendicular distance between the plane P and the origin O (0,0,0)

For this the answer is (0,0,1) apparently. Could somebody explain me why it is this??
It isn't- it can't be! "Distance" is a number, not a point or vector. In this simple case, the distance between the plane and the origin is just the distance between the points (0,0,0) and (0,0,1). Is that what you meant? What is the distance between those points?

3. Which of the points A(1,2,2), B (2,1,1), C(-1,6,2) belong to the plane P?
You plane is defined by "z= 1". Which of those points satisfy that equation?

How do I find this? Do I multiply the position vectors by the normal (0,0,1) and see if this is equal to 1?

Also does anybody know a good website explaining these type of problems because my notes and books do not cover it yet it is still in the exam!

Thanks for helping!

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