Vector components from initial and terminal points | Vectors | Precalculus | Khan Academy | Summary and Q&A

TL;DR

Learn how to find the x and y components of a vector using the coordinates of its initial and terminal points.

Key Insights

• 😥 Vectors in a coordinate plane have an initial point and a terminal point.
• 👈 The x component of a vector represents the change in x between the initial and terminal points.
• 💱 The y component of a vector represents the change in y between the initial and terminal points.
• 🇦🇪 Different notations can be used to represent vectors, such as unit vector notation, column vector notation, and numerical representation.
• ✈️ Shifting a vector in a coordinate plane does not alter its magnitude or direction, only its location.

Transcript

We can never have too much practice getting familiar with vectors. What I want to do in this video in particular, be able to relate the x and y components of a vector to the initial and terminal points to where we place it in the coordinate planes. What am I talking about? Let's say we have some vector where its initial point is here at point a and... Read More

Questions & Answers

Q: How can we find the x and y components of a vector based on its initial and terminal points?

To find the x component, subtract the initial x coordinate from the terminal x coordinate. Similarly, for the y component, subtract the initial y coordinate from the terminal y coordinate. In this case, the x component is 15 and the y component is -9.

Q: What are the different notations used to represent vectors?

There are several notations, including unit vector notation (using i and j), column vector notation (placing the components in a column), and numerical representation (directly stating the components). All these notations convey the same vector.

Q: Can vectors be placed in different locations in a coordinate plane?

Yes, vectors can be shifted around in a coordinate plane without changing their magnitude or direction. The important aspect is that the x and y components remain the same.

Q: How is the x component of a vector represented graphically?

The x component of a vector is shown as a vector that is 15 times longer than the unit vector in the horizontal direction. It extends from the initial point to the terminal point along the x-axis.

Summary & Key Takeaways

• The video explains how to determine the x and y components of a vector based on the coordinates of its initial and terminal points in a coordinate plane.

• The x component is calculated by finding the change in x between the initial and terminal points, while the y component is found by determining the change in y.

• Different notations can be used to represent vectors, including unit vector notation, column vector notation, and numerical representation.