Drawing a simple vector field issue

In summary, the conversation discusses a vector field represented by the function F(x,y,z) = yj, where j is a unit vector pointing in the same direction as the +y axis. The length of the vectors is proportional to their z coordinate, and they are parallel to the +y axis for positive z values and pointing in the opposite direction for negative z values. The conversation also clarifies the coordinates of the coordinate system and the behavior of the vectors in different planes.
  • #1
mr_coffee
1,629
1
Hello everyone I'm not sure if this is right or not...

If i have

F(x,y,z) = zj; where j is the vector, j hat.

Would that be all vectors are going to be pointing up if you assume z is up, and are in the y plane?


If the coordinate system is, z is up, y is to the right, and x is pointing at you.

If i had F(x,y,z) = yj; the answer is, No vectors emanate from the xz plane since y = 0 there. In each plane y = b, all the vectors are identical.
 
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  • #2
No. j is a unit vector pointing in the same direction as the +y axis. Which you seem to want to call 'right'. The length of the vectors is proportional to their z coordinate. What is the 'y plane'? What does 'in' a plane mean? Parallel to?
 
  • #3
I worked it out and it seems the vectors are pointing parrallel to the +y axis which is pointing right, for values > 0, and for values < 0 its pointing to the left or in the -y direction.
 
  • #4
mr_coffee said:
I worked it out and it seems the vectors are pointing parrallel to the +y axis which is pointing right, for values > 0, and for values < 0 its pointing to the left or in the -y direction.

That's the right picture (where 'values' means z, right).
 
  • #5
z is a number, j is a vector pointing in the positive y direction. Your vector field consists of vector pointing in the positive y direction, longer as z increases. (And pointing in the negative y direction for z negative.)
 

1. What is a vector field?

A vector field is a mathematical concept used to represent the direction and magnitude of a vector at each point in a given space. It can be visualized as a series of arrows, with each arrow representing the direction and strength of the vector at that particular point.

2. How do you draw a simple vector field?

To draw a simple vector field, you will need to first choose a set of points within the given space to serve as the "starting points" for your vectors. Then, using a ruler or protractor, draw arrows of equal length and direction at each point to represent the magnitude and direction of the vectors. It can be helpful to label each arrow with its corresponding coordinates.

3. What are some real-world applications of vector fields?

Vector fields have various applications in physics, engineering, and other scientific fields. They are often used to represent the flow of fluids, such as air or water, in a given space. They can also be used to model electromagnetic fields, gravitational fields, and other physical phenomena.

4. What is the difference between a scalar field and a vector field?

In a scalar field, a numerical value is assigned to each point in a given space. This value represents a physical quantity, such as temperature or pressure. In a vector field, a vector is assigned to each point, representing both magnitude and direction. This can be thought of as a combination of scalar values at each point.

5. Are there any limitations to drawing a simple vector field?

While drawing a simple vector field can help visualize the direction and magnitude of a vector at different points, it is not always an accurate representation of the actual field. In reality, the vectors may vary in magnitude and direction continuously, and a simple drawing may not be able to capture this complexity. Additionally, drawing a vector field can become more challenging when dealing with higher dimensions or non-linear systems.

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