Vector Examples in 2 Dimensions

University
Massachusetts Institute of Technology
Course
Multivariable Calculus
Pages

3

Academic year

2022
Author

Lingro
Views

17

Vector examples in 2 dimensions We draw a vector as an arrow. In this example, v is a vector, and we can describe it withtwo numbers: v1 and v2. The vector v will be written as [v1, v2]. Some people write vectors in one way, and others write them another way. You may haveseen a different notation. To illustrate, consider the vector defined by v1 times i hat plus v2 times j hat. We can alsowrite this as a vector triple product. Another notation people may have seen in high school is similar to this, but with anglebrackets instead of square or curly brackets. And the one is arrow is the one we’re gonna use. Now, if I start a vector at the origin, that's one thing. But vectors don't have to start at theorigin. So let's draw another one. Here is a vector that begins at (2, 0), and it ends at (1,1).

There is a vector v. It has a magnitude of [negative 1, 1]. If we want to write it in terms ofnumbers, what vector is that? The negative 1 comes from the change in x. From the beginning of the vector to its end, xchanged by negative 1. The vector's length, y, changed by 1 from the start of the vector to its end. Here is another vector to consider. Let us call the result w. w is also [negative 1, 1]. The x also changed by negative 1.And thechange of y is 1. So we see that w is equal to v. Thus, the two vectors are equal in length and direction, even though they begin at differentpoints.

If two vectors are equal to each other, they have the same magnitude. And they are of thesame length, and they point in the same direction. It works for these two vectors.