a. To show graphically that vector addition is commutative, let's consider two vectors, ML and LM. If vector addition is commutative, then ML + LM should result in the same vector regardless of the order in which they are added.
Let's say ML is represented by the vector from point M to point L, and LM is represented by the vector from point L to point M. When we add ML and LM, we start at point M, move to point L, and then move back to point M. This forms a closed loop, where the starting and ending points are the same. Therefore, ML + LM results in a zero vector, which means ML + LM = LM + ML = 0.
b.
- Addition: Yes, addition is commutative. For example, 3 + 5 = 5 + 3.
- Subtraction: No, subtraction is not commutative. For example, 5 - 3 ≠ 3 - 5.
- Multiplication: Yes, multiplication is commutative for real numbers. For example, 3 * 5 = 5 * 3.
- Division: No, division is not commutative. For example, 6 ÷ 3 ≠ 3 ÷ 6.
