Chapter 5.1, Problem 15SSC

(a)

To determine

The graphical proof of the commutative operation for the vector Addition.

Explanation of Solution

Introduction:

The vector addition follows the commutative relation.

The vector addition of the vectors M and L is shown below:

  

Figure (1)

Conclusion:

The figure (1) proves graphically $M+L=L+M$

(b)

To determine

The commutative operation from the arithmetic operations.

Answer to Problem 15SSC

The arithmetic operations addition and multiplication are commutative.

Explanation of Solution

Introduction:

The arithmetic operation in which the result of the operation remains unaffected on reversing the order of the variables is called the commutative operations.

Let the two algebraic numbers are 4 and 3. The arithmetic operations for these numbers are following:

Addition: $4+3=3+4=7$

Subtraction: $4-3\ne 3-4$

Multiplication: $4\times 3=3\times 4=12$

Division: 12 $\frac{4}{3}\ne \frac{3}{4}$

The result for only addition and multiplication remains unaffected on reversing the order of the numbers 4 and 3.

Conclusion:

Thus, the arithmetic operations addition and multiplication are commutative.