Question

Show that the order of addition of three vectors does not affect their sum. Show this property by choosing any three vectors A, B, and C, all having different lengths and directions. Find the sum A + B + C, then find their sum when added in a different order and show the result is the same. (There are five other orders in which A, B, and C can be added; choose only one.)

The order of adding three vectors A, B, and C affects their sum.
1. True
2. False

Answer 1

The order of addition of three vectors does not affect their sum. Vector addition is commutative.

Step-by-step explanation:

Vector addition is commutative, which means that the order in which you add vectors does not affect their sum. This property can be demonstrated by choosing any three vectors A, B, and C with different lengths and directions.

For example, let's say we have vector A = (2, 0), vector B = (0, 3), and vector C = (4, 1). The sum of A, B, and C is A + B + C = (2, 0) + (0, 3) + (4, 1) = (6, 4).

If we add the same three vectors in a different order, say B + C + A, we get (0, 3) + (4, 1) + (2, 0) = (6, 4). The result is the same as before, showing that the order of addition does not affect the sum of the vectors. Hence it is false.