Adding and subtracting vectors

TL;DR

Learn how to add and subtract two-dimensional vectors by combining or subtracting their corresponding components.

Transcript

• [Voiceover] So let's get some practice and hopefully a little bit of intuition for adding and subtracting two dimensional vectors. So let's say that I have vector A, and let's say that its x component is I don't know, three, and it's y component is negative one. And let's say we also have a vector B. Vector B, and let's say that its x component i... Read More

Key Insights

• 🪜 Two-dimensional vectors can be added or subtracted by combining or subtracting their corresponding components.
• 🆘 Shifting one vector can help visualize the addition or subtraction of vectors.
• ❣️ Addition and subtraction of vectors follow specific conventions for combining or subtracting their x and y components.

Questions & Answers

Q: How do you add two-dimensional vectors?

To add two-dimensional vectors, add their x components together and their y components together. This will give you the resulting vector.

Q: How do you subtract two-dimensional vectors?

To subtract two-dimensional vectors, subtract the x components and the y components of one vector from the corresponding components of the other vector.

Q: Can vectors be shifted in a visual representation?

Yes, vectors can be shifted in a visual representation as long as their magnitude and direction remain the same.

Q: What is the result when adding the vectors A and B with the components given?

Adding the vectors A and B, with components (3, -1) and (2, 3) respectively, will result in a vector with components (5, 2).

Summary & Key Takeaways

• Two-dimensional vectors can be added by simply adding their x components together and their y components together.

• Similarly, to subtract two-dimensional vectors, subtract the x components and the y components separately.

• Visualizing the addition or subtraction of vectors can be done by shifting one vector so that its initial point is at the terminal point of the other vector.