Solve Vector Equation: iy + jx & (i + j)/√2

[astroman707]

TL;DR Summary

"Using arrows of the proper magnitude and direction, sketch each of the following vector functions: (a) iy + jx

I'm reading div grad curl for my math methods class, and I came across this question:
"Using arrows of the proper magnitude and direction, sketch each of the following vector functions: (a) iy + jx, (b) (i + j)/√2
I don't understand the notation. Why is there an y and x next to the i and j in (a), and why doesn't (b) have x or y?

 

[jedishrfu]

The x,y are the position of the vector tail in the XY plane the i,j are the unit vectors with i pointing along the X axis and j pointing along the Y axis.

So say you are at point (2,7) in 2D space then the vector at the point which can point in any direction in the xy plane is described as being 7i + 2j for the (a) function.

Take out some graph paper and select some points and then draw the vector tail as originating at that point going off in the direction of yi +xj

Check out DESMOS graphing calculator. It can help with the graphing.

https://www.desmos.com/calculator/eijhparfmd
also Geogebra can plot it too:

https://www.geogebra.org/m/QPE4PaDZ
The cool thing of course is you can try different variations to see how they plot and test your knowledge and intuition with these calculators.

 

[jedishrfu]

For (b), the equation is after using the distributive law:

$\frac {1} {\sqrt 2)} i + \frac {1} {\sqrt 2} j$

 

[jtbell]

Why is there an y and x next to the i and j in (a), and why doesn't (b) have x or y?

In (a), the (vector) value of the function is different for each point (x,y).

In (b), the (vector) value of the function is the same for each point (x,y). In other words, it’s a constant function.