# Finding a vector perpendicular to a plane

• Miike012
In summary, it doesn't matter if you calculate PQ x PR or PR x PQ as any vector perpendicular to the plane will do. Similarly, RP x RQ was not chosen because any two vectors in the plane that are not parallel will result in a third perpendicular vector. When finding u x v x w, it is likely that they associate left-to-right and calculate (u x v) x w.

#### Miike012

How did they know to do PQ cross PR instead of PR cross PQ?
And why did they not choose RP cross RQ?

Look at picture.

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Miike012 said:
How did they know to do PQ cross PR instead of PR cross PQ?
Since any vector that is perpendicular to the plane will do, it doesn't matter if they calculate PQ X PR or PR X PQ, which will just point the opposite direction.
Miike012 said:
And why did they not choose RP cross RQ?

Look at picture.

If you cross any two vectors in the plane that aren't parallel, you'll get a third vector that is perpendicular to the first two.

Another question:
if I have 3 vectors u,v, and w
If i am trying to find u cross v cross w do i cross u with v first then w or v cross w then u?

I'm pretty sure they associate left-to-right, so u X v X w would be the same as (u X v) X w.

## 1. What is a vector perpendicular to a plane?

A vector perpendicular to a plane is a vector that is at a 90-degree angle to the plane and intersects it at a single point.

## 2. How do you find a vector perpendicular to a plane?

To find a vector perpendicular to a plane, you can use the cross product between two non-parallel vectors that lie on the plane. The resulting vector will be perpendicular to both of the original vectors and therefore perpendicular to the plane.

## 3. Can a vector be perpendicular to more than one plane?

Yes, a vector can be perpendicular to more than one plane as long as it is at a 90-degree angle to both planes.

## 4. Is a vector perpendicular to a plane unique?

No, a vector perpendicular to a plane is not unique. There are infinite possible vectors that can be perpendicular to a given plane.

## 5. Why is finding a vector perpendicular to a plane important?

Finding a vector perpendicular to a plane is important because it can be used to solve various mathematical and scientific problems, such as determining the direction of motion for an object in three-dimensional space or calculating the normal force on an object resting on a plane.