Vector examples in 2 dimensions
We draw a vector as an arrow. In this example, v is a vector, and we can describe it with two numbers: v1 and v2. [Graph] The vector v will be written as [vi, v2]. v->=(v_1,v_2) Some people write vectors in one way, and others write them another way. You may have seen a different notation To illustrate, consider the vector defined by v1 times i hat plus v2 times j hat. We can also write this as a vector triple product. v->=v_1i+v_2j Another notation people may have seen in high school is similar to this, but with angle brackets instead of square or curly brackets. ⟨v_1,v_2⟩ 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 the origin. So let’s draw another one. Here is a vector that begins at (2, 0), and it ends at (1, 1). [Graph] There is a vector v. It has a magnitude of [negative 1, 1]. If we want to write it in terms of numbers, what vector is that? v-> = (- 1, 1) The negative 1 comes from the change in x. From the beginning of the vector to its end, × changed 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. [Graph] Let us call the result w. w is also [negative 1, 1]. The x also changed by negative 1.And the change of y is 1. So we see that w is equal to v. W-> = (- 1, 1) = v-> Thus, the two vectors are equal in length and direction, even though they begin at different points. If two vectors are equal to each other, they have the same magnitude. And they are of the same length, and they point in the same direction. It works for these two vectors.
