Final answer:
In vector addition, the operations are commutative (vectors can be added in any order), and the result is independent of the starting point, but the magnitude of the result is not always the sum of the magnitudes of the individual vectors.
Step-by-step explanation:
The question pertains to the properties of vector addition. Several statements are provided, and we must determine which are true. Let us evaluate each statement:
- A) Vectors can be added in any order: This is true. Vector addition is commutative, which means A + B = B + A. This property is confirmed through demonstrations that the resultant vector remains consistent regardless of the order in which the vectors are added.
- B) The result of vector addition is independent of the initial point: This is also true. When vectors are added graphically, the starting position can vary, but the final resultant vector will be the same regardless of where you begin.
- C) Adding vectors is a commutative operation: Again, this is true. As explained before, the order in which vectors are added does not affect the sum.
- D) The magnitude of the result is always equal to the sum of the magnitudes of the vectors being added: This statement is false. The resultant vector's magnitude is not necessarily the sum of the magnitudes of the individual vectors, especially when the vectors are not aligned in the same direction.