Question about direction of Moments 3d

[baird.lindsay]

Homework Statement

knowing the tension in cable AB is 570 N, determine the moment about each of the coordinate axes of the force exerted on the plate at B . This link has a picture http://www.chegg.com/homework-help/questions-and-answers/knowing-tension-cable-ab-570-n-determine-moment-coordinate-axes-force-exerted-plate-b-q3031608

My question is when I am doing the cross product I do r X F . so <900, 0,0> X <450, -350, -180>

Instead of Fsub AB I do F sub BA so < 900,0,0> X < -450, 350,180> and I get an answer the opposite sign. Does it matter which way I find the force vector? and are both answer equivalent?

162j-270K or -162j +270K

I know how to solve the problem I just don't understand why you can use the tension from AB or BA because the answer will have different signs.

Homework Equations

r X F

The Attempt at a Solution

 

[SteamKing]

Yes, it does make a difference.

The force vector in your first cross product is incorrect, but it is correct in the second cross product.
The correct force vector for the tension in AB must have a negative x-component.

 

[baird.lindsay]

Yes, it does make a difference.

The force vector in your first cross product is incorrect, but it is correct in the second cross product.
The correct force vector for the tension in AB must have a negative x-component.

Why does it have to have a negative x component?

Unit Vector BA =< -450, 300, 180>
Unit Vector AB=< 450, -300, -180>

My solution manual is using BA but my teacher is saying it doesn't matter so I am confused. Please explain.. Thanks in advance:)

 

[SteamKing]

It matters because you have a tension in line AB. This tension is acting to hold the plate up. If you substituted vector AB, then that force would tend to push the plate in the opposite direction, below the x-axis.

Are you sure your teacher is saying the direction of the force vector doesn't matter?

 

[rezeew]

I would like to clarify that the direction of the moment is dependent on the choice of coordinate system. In this case, the homework statement does not specify a specific coordinate system, so either direction is acceptable as long as it is consistent throughout the problem.

In terms of finding the force vector, it is important to note that the cross product is not commutative, meaning that the order of the vectors does matter. So when finding the moment, it is important to use the correct order of the vectors. In this case, using either F_AB or F_BA will result in different signs because the vectors are in opposite directions. However, both answers are equivalent in terms of magnitude, so either one can be used as long as it is consistent throughout the problem.

It is also important to note that the direction of the moment is dependent on the choice of coordinate system, so the sign of the answer may change depending on the chosen coordinate system. Therefore, it is important to clearly define the coordinate system in the problem statement to avoid confusion.