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

• I
• astroman707
In summary, the conversation discusses the notation and interpretation of vector functions in the context of div grad curl. The first function (a) is dependent on the position of the vector tail in the XY plane, while the second function (b) is a constant function. The use of graphing calculators such as DESMOS and Geogebra is recommended to visualize and explore different variations of these vector functions.
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?

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:

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.

Delta2

## 1. What is a vector equation?

A vector equation is an equation that involves vectors, which are mathematical objects that have both magnitude and direction. Vectors can be represented using components, such as x and y, or using unit vectors, such as i and j.

## 2. What does "iy + jx" mean in the vector equation?

The expression "iy + jx" represents the vector iy in terms of its components. This means that the vector has a magnitude of y in the y-direction and a magnitude of x in the x-direction.

## 3. What does "(i + j)/√2" represent in the vector equation?

The expression "(i + j)/√2" represents a unit vector in the direction of the vector i + j. This means that the vector has a magnitude of 1 and is pointing in the direction of i + j.

## 4. How do you solve a vector equation?

To solve a vector equation, you need to isolate the variable that you are solving for. This can be done by using algebraic operations, such as addition, subtraction, multiplication, and division, on both sides of the equation. It is important to keep in mind the properties of vectors, such as commutativity and distributivity, when solving a vector equation.

## 5. What is the significance of the √2 in the vector equation?

The √2 in the vector equation represents the magnitude of the unit vector. In this case, the unit vector has a magnitude of √2, which means that its components are i/√2 and j/√2. This is because the magnitude of a unit vector is always equal to 1, and in this case, the magnitude of the vector i + j is √2.

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