Finding Direction of Vector A: M & N Intersect Perpendicularly

[phiby]

Given this line

M & N are two vectors which intersect and are perpendicular to each other.

1) Chose A to be orthogonal to N & M.

or

2) Chose A to be perpendicular to the plane in which both M & N lie.

Do the above descriptions indicate the direction of A - i.e. there are 2 possible directions.
Do either of these descriptions give the direction of A? i.e. for a plane, there are 2 opposite vectors which can both be considered perpendicular to the plane.

In either of these (1 & 2), does changing the order of M and N indicate a different direction?

 

[algebrat]

no

no

 

[ME_student]

no

no

Why?

 

[chiro]

Why?

Because you have not supplied any orientation details. You would only have a direction if you supplied a specific orientation.

The cross product can be visualized using the right hand rule where your first vector is your thumb, the second your fingers and the result will be in the direction extending from your palm outward.

In this particular case, the orientation is not just the vectors themselves, but the ordering of those vectors that correspond to their placement in the cross product.

Once you specify an orientation, you will then have the orientation for the surface (i.e. the plane), but until then, you don't have an orientation.

If you want to understand orientation, you can read books on vector calculus and geometric algebra and they will give you a deeper insight into this, but for the time being just be aware that unless you provide an orientation, you won't be able to determine what you need to determine.

 

[Studiot]

Wry smile as 'Chiro' expounds on 'Chirality'.

Note also that depending upon your definition of vector there are possibly many vectors satisfying condition 2 as you have not specified concurrency.

 

[ME_student]

Because you have not supplied any orientation details. You would only have a direction if you supplied a specific orientation.

The cross product can be visualized using the right hand rule where your first vector is your thumb, the second your fingers and the result will be in the direction extending from your palm outward.

In this particular case, the orientation is not just the vectors themselves, but the ordering of those vectors that correspond to their placement in the cross product.

Once you specify an orientation, you will then have the orientation for the surface (i.e. the plane), but until then, you don't have an orientation.

If you want to understand orientation, you can read books on vector calculus and geometric algebra and they will give you a deeper insight into this, but for the time being just be aware that unless you provide an orientation, you won't be able to determine what you need to determine.

I was just curious. We recently touched up on Vectors in my math course a bit.