Vectors AB+BC+AC is a) vector CAb) vector 0c) vector BAd) vector AC?
Understanding Vectors
Vectors are fundamental in physics and mathematics, representing quantities with both magnitude and direction. In this case, we are analyzing the vector sum of AB, BC, and AC.
Vector Representation
- Let A, B, and C be points in space.
- Vectors can be visualized as arrows pointing from one point to another.
Breaking Down the Sum
- AB is the vector from point A to point B.
- BC is the vector from point B to point C.
- AC is the vector from point A to point C.
Thus, the expression AB + BC + AC can be interpreted as follows:
Vector Addition
- According to the triangle law of vector addition, if you place the tail of vector BC at the head of vector AB, the resultant vector will point directly from A to C.
- Adding vector AC (which directly connects A and C) does not change the overall direction; it simply reinforces the addition of the two.
Conclusion
- When you calculate AB + BC, the result is AC.
- Therefore, including AC in the sum does not change the overall vector result.
Final Answer
- The expression AB + BC + AC = 0. This implies that the vectors form a closed triangle, with no net displacement.
Hence, the correct answer is (b) vector 0, as the vectors effectively cancel each other out, leading to no net movement.
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