# Find vector parallel to two planes

• Bestphysics112
In summary: Otherwise, you can simply stop responding to the thread.In summary, the conversation discusses finding unit vectors parallel to two given planes. The suggested approach is to find the normal of both planes and take the cross product to obtain a resultant vector that is parallel to both planes. The final step is to normalize the vector to obtain the unit vector. The use of LaTeX is recommended for more advanced math discussions on the forum. The thread cannot be closed, but it can be marked as solved in the homework sections.
Bestphysics112

## Homework Statement

Find unit vector(s) that are parallel to both of the planes 6x + y + z = 1 and x − y − z = 0 .

N/A

## The Attempt at a Solution

OK. So here is my reasoning - I find the normal of both the given planes and find the cross product between the vectors. The resultant vector will be parallel to both of the planes. I normalize the vector after to obtain the final answer. Is my logic correct? This is my first post on PF so I'm not sure if there is anything else I need to provide

Bestphysics112 said:
Is my logic correct?
Yes.

Orodruin said:
Yes.
Thanks. Is LaTeX necessary for this forum? I will probably ask some questions in the physics sections soon and was wondering what formatting is preferred. Also how do i close this thread?

Bestphysics112 said:
Is LaTeX necessary for this forum?
I would highly recommend it for more advanced maths. For simple things there is no point really. There is a short introduction on how to use it on the forum here: LaTeX Primer

Bestphysics112 said:
Also how do i close this thread?
You cannot close the thread. In the homework sections, you can mark a thread as solved by clicking "mark solved" in the upper right corner.

## 1. What is a vector parallel to two planes?

A vector parallel to two planes is a vector that lies in the same direction as both planes and does not intersect either of them. It is perpendicular to the normal vectors of both planes.

## 2. How do you find a vector parallel to two planes?

To find a vector parallel to two planes, you can first find the normal vectors of both planes. Then, take the cross product of the two normal vectors to get a vector that is perpendicular to both of them. This vector will be parallel to both planes.

## 3. Why is finding a vector parallel to two planes important?

Finding a vector parallel to two planes is important in many applications, such as solving systems of linear equations and calculating the direction of a line or plane. It can also be used in physics and engineering to determine the direction of forces acting on an object.

## 4. Can there be more than one vector parallel to two planes?

Yes, there can be infinitely many vectors parallel to two planes. This is because the cross product of two vectors can produce a vector with different magnitudes as long as it is in the same direction. Any multiple of the resulting vector will also be parallel to the two planes.

## 5. Is it possible for two planes to have no vector parallel to them?

Yes, it is possible for two planes to have no vector parallel to them. This can happen when the two planes are parallel to each other, meaning they have the same normal vector. In this case, any vector that is parallel to one plane will also be parallel to the other plane.

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