Chapter 11 - Vectors and Vector-Valued Functions - 11.1 Vectors in the Plane - 11.1 Exercises - Page 767: 6

Triangle Rule or Parallelogram Rule

We can use one of the two methods: Triangle Rule or Parallelogram Rule. For Triangle Rule, if we have to add vectors $a$ and $b$, first we translate one of the vectors (let's say $b$) so that the tail of $b$ gets into the head of $a$. Then we connect the tail of $a$ to the head of $b$. The sum $a+b$ is the vector which extends from the tail of $a$ to the head of $b$. For the Parallelogram rule, first we translate one of the vectors so that they have the same tail. We draw a parallelogram in which the two vectors sharing the same tail represent two adjacent sides. The sum $a+b$ is the diagonal of the parallelogram which begins at the tails of $a$ and $b$. This method works if the vectors $a$ and $b$ are not parallel.