Vector Addition and Subtraction: Formulas and Examples

University
Massachusetts Institute of Technology
Course
Multivariable Calculus
Pages

2

Academic year

2023
Author

Sporkz
Views

73

Adding vectors ● Vector addition is the process of adding two or more vectors.● The result of vector addition is a vector that has the same direction as the initial vectors, but whose length is equal to the sum of their lengths. ● Vector subtraction is similar to vector addition, except that the negative sign (-) is used instead of a plus (+) sign. The sum of two vectors is the vector that results when their initial directions are combined. Now we have vector v, vector w, and we add. First, I take w and make a copy of it that starts at the end of v. This new copy is also w. As we saw earlier, two vectors are the same as long as their lengths are the same andtheir orientations are the same (they point in the same direction). So this is also w. Now, there is a vector that goes from the start of v to the end of w here. That vector isequal to v plus w.

In addition, there is a formula for v plus w that can be derived by examining thecomponents in the picture. Let's say that this is v and this is w. This here is v1, and this is w1. And this is w1. I can justpush it down. And that's also w1. This one is w2. And those are the same. And there is v2.v plus w is that vector. Now we ask what is the change in x when going from here to here? It's v1 plus w1.Therefore, the change in y is v2 plus w2. Thus, it is pretty simple formula. Here, v1 plus w1, v2 plus w2. One more question about vector adding. Suppose you have vectors v and w. Then, a vector going from the end of v to the end of wis drawn. The question is, what does that vector equal? Which of the following is true: v − w, w − v, or v + w?