Performing Operations on Vectors in the Plane

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  • 0:02 Vectors
  • 1:41 Adding
  • 2:51 Subtracting
  • 4:10 Multiplication
  • 4:39 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.


All right, let's go!

We talk about vectors in this video lesson. What are they? We define them as measurements that include both magnitude and direction. Just think of an arrow. We can draw arrows of different lengths, but each arrow has its own direction. This is exactly what a vector is.

And guess what? We draw them on our Cartesian plane; they look just like our arrows. Remember how we write our points on the Cartesian plane with parentheses and then our values separated by commas? Our points look like (3, 4) with our x value first and then our y value (x, y).

We write our vectors similarly, as well. When we draw our vectors on our Cartesian plane, we usually have the vector beginning at the point (0, 0) and we mark the point where the vector ends. We mark the end point the same way we mark our Cartesian points with our x value first and the y value second. So, we label a vector that starts at the point (0, 0) and ends at the point (5, 6) with the notation (5, 6) to let us know that it has an x length of 5 and a y length of 6.

Most times you will see vectors identified with just two values, but sometimes you will see vectors being identified with more than two values. Theoretically, vectors can be identified with as many values as needed. We could have a vector identified with 3 or even 5 values. For example, (x, y, z) or even (1, 2, 3, 4, 5).


Using this notation for our vectors, we can easily perform our operations of addition, subtraction, and multiplication. These vector operations become very easy when we break the notation apart into the vector's separate parts. Even though our vectors may have two or more numbers that identify them, when we do the operations, we do it in stages. First, we add, subtract, or multiply just the x values. Then we add, subtract, or multiply just the y values, and so on and so forth until we've covered all our identifying values.

Let's look at addition.

Add vector A (1, 2) and vector B (5, 8).

To add these two vectors, we separate each vector into its x part and its y part. For vector A, our x is 1 and our y is 2. For vector B, our x is 5 and our y is 8. Adding them, we get A + B = (1 + 5, 2 + 8) = (6, 10). Do you see how we simply added the two vectors in parts? That's all we have to do. The addition part is the same as we've always done it.


Subtraction is also very similar. We break the two vectors into their separate parts and then perform a subtraction on each of the parts.

Subtract vector A (5, 6) from vector B (11, 23).

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