Question

3. (1) The three vectors in Fig. 3 32 can be added in six

different orders (V, + V: + V. V. + V, + V, etc.).
Show on a diagram that the same resultant is ob.
tained no matter what the order.

Answer 1

cannot do diagrams on here sorry :)

Answer 2

1. The commutative property of vector addition states that the order in which vectors are added does not affect the result.

2. When adding three vectors A, B, and C, the resultant vector remains the same, regardless of the order in which they are added.

3. This property can be visually demonstrated by drawing arrows representing the vectors and showing that different orders yield the same final result.

Step-by-step explanation:

The commutative property of vector addition asserts that the order in which vectors are added does not alter the ultimate result. Consider three vectors, A, B, and C. When visually representing these vectors as arrows, their sum remains constant, regardless of the sequence in which they are combined. To illustrate, start with vector A and add vector B, resulting in a vector AB.

Subsequently, add vector C to the tip of AB, forming the ultimate sum of A, B, and C. Conversely, initiating the addition with vector B and then adding vector A yields the same vector AB as the result. Further addition of vector C to this result still produces the identical outcome. This phenomenon can be graphically depicted by drawing arrows representing the vectors in different sequences but culminating in the same resultant vector.

This property is fundamental in vector algebra, providing a mathematical foundation for diverse applications, from physics to computer graphics, where vector operations play a crucial role in describing and manipulating spatial relationships.