How to Sketch a Vector Valued Function and Find Orientation and Rectangular Form | Summary and Q&A

TL;DR

Learn how to graph vector valued functions and determine their orientation using rectangular form and a simple table.

Key Insights

• 😑 Vector valued functions with straight lines can be expressed in rectangular form, making graphing easier.
• 🔌 Plugging in values of T and observing the corresponding X and Y components helps in understanding the shape of the graph.
• 👻 Rectangular form allows for solving equations simultaneously and simplifies the process of finding the orientation.
• ❓ The orientation of a graphed vector valued function can be determined by analyzing the direction of the plot and whether it is increasing or decreasing.
• ⌛ Creating a table with increasing values of T helps visualize the movement of the vector over time.
• 💁 Using the rectangular form and table method, it is possible to accurately graph and determine the orientation of vector valued functions.
• 🏑 Graphing vector valued functions is a useful tool in various fields, such as physics and engineering.

Transcript

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Questions & Answers

Q: How do you graph a vector valued function?

To graph a vector valued function, plug in values of T and plot the corresponding X and Y components. Connect the points to create a line representing the function.

Q: What is rectangular form in vector valued functions?

Rectangular form in vector valued functions involves expressing the X component as the equation T/8 and the Y component as the equation T - 1. This form facilitates graphing and calculations.

Q: How do you find the orientation of a graphed vector valued function?

To determine the orientation, create a table with increasing values of T and calculate the corresponding X and Y components. Observe the direction in which the vector is moving to determine the orientation of the graph.

Q: Can you explain the process of graphing vector valued functions in rectangular form further?

To graph in rectangular form, solve for T in one equation (T = 8X) and substitute it into the other equation (Y = 8X - 1). Plot the coordinates on the X-Y plane and connect the dots to form a line. Remember to use arrows to indicate the orientation.

Summary & Key Takeaways

• A vector valued function is graphed by plugging in values of T and plotting the corresponding X and Y components.

• To graph in rectangular form, solve for T in one equation and substitute it into the other equation.

• To determine the orientation, create a table with increasing values of T and observe the direction of the graph.