Understanding Vector Addition
Vectors are quantities that have both magnitude and direction. The addition of vectors follows specific rules, particularly in relation to their order.
Vector Notation
- Let A and B be two vectors.
- AB denotes the vector from point A to point B.
- BA denotes the vector from point B to point A.
Properties of Vector Addition
- Vector addition is commutative, which means that the order of addition does not affect the result: AB + BA = BA + AB.
- The vector BA can be expressed as the negative of vector AB: BA = -AB.
Calculating AB + BA
- Given AB + BA, we can substitute BA with -AB:
- AB + BA = AB + (-AB) = AB - AB = 0.
Conclusion
From the calculations and properties of vector addition, we conclude:
- The expression AB + BA results in the zero vector, represented as Vector 0.
Final Answer
- The correct choice is: b) Vector 0.
This insight reinforces the fundamental concept that the addition of a vector and its negative yields a null result, showcasing the balance inherent in vector mathematics.