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Make a sketch in the x - y plane, of the listed vector functions. Plot enough different vectors...

Question:

Make a sketch in the x - y plane, of the listed vector functions. Plot enough different vectors to get a feeling for what this field looks like in the x - y plane.

1. {eq}y \hat x {/eq}

2. {eq}r \hat r {/eq} (The symbol r here refers to the usual r in spherical coordinates)

3. {eq}\frac{x}{\sqrt {x^2 + y^2}} \hat x + \frac{y}{ \sqrt { x^2 + y^2}} \hat y {/eq} Also explain in words what this plot is showing.

Vector Fields:

Recall that a vector field is a function that assigns a vector to every point in a space. So to plot a vector field, we plot some representative vectors at some points. This is often best accomplished by simply putting the tip of pencil at a point, and just mentally computing what the vector should be.

Answer and Explanation: 1

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The field is {eq}\vec F = y\ \hat x = \left< y, 0 \right> {/eq}, so at every point, the tip of the vector is placed {eq}y {/eq} horizontal...

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Vectors: Definition, Types & Examples

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Chapter 57 / Lesson 3
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In this lesson, learn what vectors are and how to represent them mathematically. You will also learn how to tell if two vectors are equal, parallel, collinear, or coplanar.


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