Graphing 2D Vector Fields with Calc Plot 3D

This lesson demonstrates how to graph 2D vector fields using Calc Plot 3D. It covers the process of entering vector components, customizing the graph by adjusting vector scaling and density, and graphing various vector fields with different mathematical expressions. The tutorial also highlights features like flow lines and color customization, providing a comprehensive guide to visualizing vector fields effectively.

What is the first step in graphing a vector field using Calc Plot 3D?

• Select a color for the vectors

• Adjust the scaling

• Clear the default graph

• Enter the vector components

How do you enter the x component for the first vector field?

• m = 0

• m = -x

• m = y

• m = x

What happens when you change the scaling factor from 4 to 2?

• Vectors disappear

• Vectors get shorter

• Vectors get longer

• Vectors change color

What is the y component for the second vector field?

• y = -x

• y = 1

• y = x

• y = 0

How can you change the color of the vectors in the graph?

• By selecting a different graph type

• By changing the vector components

• By clicking the bar next to n and p

• By adjusting the scaling

What is the x component of the complex vector field?

• x^2 - y^2 - 4

• x^2 - y^2 + 4

• x^2 + y^2 + 4

• x^2 + y^2 - 4

What is the effect of changing the scaling factor to 8 for the complex vector field?

• Vectors disappear

• Vectors become longer

• Vectors become shorter

• Vectors change direction

What is the x component of the final vector field?

• cos(x + y)

• cos(x - y)

• sin(x + y)

• sin(x - y)

How do you adjust the vector lengths in the final vector field?

• By changing the vector components

• By changing the graph type

• By adjusting the scaling factor

• By selecting a different color

What is the purpose of observing flow lines in a vector field?

• To adjust the scaling

• To understand the direction of vectors

• To clear the graph

• To change the vector color