Question

part c
in parts a and b, you added the same two vectors. but you added them in a different order each time. how do your steps in answering parts a and b compare? what was different about them? did they result in the same vector?

Explanation:

This problem is about vector addition, specifically the commutative property of vector addition. In vector addition, the order of adding two vectors (let's say $\vec{A}$ and $\vec{B}$) doesn't matter, i.e., $\vec{A}+\vec{B}=\vec{B}+\vec{A}$. So when comparing the steps in parts A and B (where the same two vectors are added in different orders), the main difference would be the order in which the vectors are taken for addition (e.g., first vector 1 then vector 2 in part A, and first vector 2 then vector 1 in part B). However, because of the commutative property of vector addition, the resultant vector (the sum) should be the same in both cases. The steps for adding vectors (like breaking into components, adding corresponding components, then finding the magnitude and direction of the resultant) would follow the same general process, but the order of the vectors in the addition operation is reversed.

Answer:

The steps for adding the vectors follow the same general process (e.g., component - by - component addition, then finding the magnitude and direction of the resultant). The difference is the order in which the two vectors are added. Due to the commutative property of vector addition ($\vec{u}+\vec{v}=\vec{v}+\vec{u}$), they result in the same vector.