How Do You Visualize a Vector Field Like v(x, y) = (2.5, -x)?

[hexa]

Please could someone explain to me how to visualise a vector field? Let's say it's v(x, y) = (2.5, -x) on whatever domain. I tried it the same way as I would visualize a scalar field but the results did not correspondent at all with the results I'd expect.

The same for drawing the field along the x and y-axis and along lines through the middle that make a 45 degree angle with x and y. Again my results look somewhat weired...

Thanks a lot,
hexa

 

[HallsofIvy]

If v= (2.5, -x) then the x-component is 2.5 while the y component is -x. Every such vector is constant along a vertical x= a line.

Along the y-axis, for example, all vectors are (-2.5,0), pointing parallel to the negative x-axis with length 2.5. Along the line x= 1, all vectors are (-2.5, -1), now pointing down and to the left. Along the line x= 2, all vectors are (-2.5,-2), pointing left but even more "down". Along the line x= -1, all vectors are (-2.5, 1) pointing up and to the left.

It's much easier to draw the field along "isoclines" where the vector is a constant (here x= constant which includes x=0, the y-axis) but if you must draw along the x-axis, you get vectors that always have -2.5 x-component but y-component larger and larger: Think of a vector starting of pointing straight back but swinging more and more downward as you move along the positive x axis. Of course, the vector swings more and more upward as you move left along the negative x-axis. As far as the lines y= x, y= -x, just look down to the x-axis. The vector at a point on either y= x or y= -x looks exactly like the vector on the x-axis directly below or above the given point.