Final answer:
The order of vector addition does not affect their sum, demonstrated by adding three vectors with different lengths and directions both algebraically and graphically. This is due to the commutative property of vector addition.
Step-by-step explanation:
The question involves the concept of vector addition, which is part of Physics and Mathematics, particularly when discussing vector properties. To demonstrate that the order of addition does not affect the sum of the vectors, we can use an example involving three vectors A, B, and C. For instance, let's consider three vectors with different lengths and directions:
- Vector A: (2, 3)
- Vector B: (1, -1)
- Vector C: (-1, 2)
Adding these vectors in the order A + B + C, we get the resultant vector R: (2+1-1, 3-1+2) = (2, 4).
If we change the order and add them as B + C + A, the resultant vector R' will be the same: (1-1+2, -1+2+3) = (2, 4). This shows that vector addition is commutative.
Moreover, by using the head-to-tail method or algebraic methods, we affirm that regardless of the order in which vectors are added, the resultant vector remains the same, which is a fundamental property of vectors.