Final answer:
The question is about demonstrating the commutative property of vector addition by showing that the sum of vectors a, b, and c will remain the same irrespective of the order in which they are added.
Step-by-step explanation:
The original question asks to show that the order of addition of three vectors does not affect their sum. To prove this, consider three non-collinear points A, B, and C, with position vectors a, b, and c, respectively.
By the commutative property of vector addition, we know that A + B + C is the same as adding the vectors in any other order, for example, B + C + A or C + A + B.
To demonstrate, we'll add the vectors in the order given and then in one other order and show that both results are the same, confirming that vector addition is commutative.
When we add vectors using analytical methods, we usually break them down into their perpendicular components along the x, y, and z axes. Then we add the respective components to get the resultant vector R.