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

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Discussion Overview

The discussion revolves around understanding vector functions, specifically the expressions iy + jx and (i + j)/√2. Participants explore the notation and implications of these vector representations in the context of a math methods class, focusing on their graphical representation and underlying concepts.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant questions the notation of the vector functions, specifically why there are variables y and x associated with i and j in the first function, and why the second function lacks these variables.
  • Another participant explains that x and y represent the position of the vector tail in the XY plane, while i and j are unit vectors along the X and Y axes, respectively.
  • A suggestion is made to use graphing tools like DESMOS and Geogebra to visualize the vectors and enhance understanding.
  • It is noted that the first function (a) varies based on the position (x,y), while the second function (b) represents a constant vector value across all points in the XY plane.

Areas of Agreement / Disagreement

Participants generally agree on the interpretation of the vector functions, but there is some uncertainty regarding the implications of the constant nature of the second function compared to the first. The discussion remains exploratory without a definitive resolution on all points raised.

Contextual Notes

Some assumptions about the understanding of vector notation and graphing techniques may be implicit in the discussion. The distinction between variable and constant vector functions is highlighted but not fully resolved in terms of its broader implications.

astroman707
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TL;DR
"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?
 
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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.
 
For (b), the equation is after using the distributive law:

##\frac {1} {\sqrt 2)} i + \frac {1} {\sqrt 2} j##
 
astroman707 said:
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.
 
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