Chapter 8.7, Problem 46HP

To determine

To explain:

The comparison and contrast method of addition of vectors in parallelogram and triangle

Answer to Problem 46HP

Addition of two vectors in parallelogram and triangle result in the same answer and essentially are the same.

The difference is that the parallelogram method you put the both initial points together where the triangle method you start the second vector at the terminal point of the first.

Explanation of Solution

In order to draw $\overline{a}+\overline{b}$ , one can translate $\overline{b}$ so that the tail of touches the tail of $\overline{a}$ . Complete the parallelogram. Then, draw the resultant vector from the common tail to the $\overline{a}+\overline{b}$ vertex opposite in the parallelogram.

The resultant vector is represented by a diagonal of the resulting parallelogram:

  

In order to draw $\overline{a}+\overline{b}$ , one can translate $\overline{b}$ so that the tail of touches the tip of $\overline{b}$ . Then, draw the vector resultant $\overline{a}+\overline{b}$ from the tail of $\overline{a}$ to the tip of $\overline{b}$ . The resultant vector is represented by the remaining side which is nothing but third side of the triangle.

Addition of two vectors in parallelogram and triangle result in the same answer and essentially are the same. The parallelogram method takes advantage of the fact that opposite sides of a parallelogram are congruent.

The difference is that the parallelogram method you put the both initial points together where the triangle method you start the second vector at the terminal point of the first.