Question

Question #82570

Answer 1

They're useful in vector addition.

Explanation:

Adding vectors is a concept that one will be using throughout their physics career, so understanding the concepts of vector addition is vital:) These two laws are similar; here's what they are:

The triangle law of vector addition states that if two vectors (which we'll call `vecA` and `vecB`) are positioned head to tail, the sum of them is the line connecting the two of them, that would form a triangle:

where `vecR` is called the resultant vector. The order of which vector is placed at the head of which vector doesn't matter, which is proven by the parallelogram law.

The parallelogram law of vector addition states that when two vectors (`vecA` and `vecB`) are placed head to tail, they form two adjacent sides of a parallelogram, and the sum of them is the diagonal of the parallelogram they form:

Notice that the parallelogram they form is also just two trianglular vector sums, each triangle starting with a different vector. This proves that vector addition obeys the commutative law of addition, and that their order doesn't matter.