Physics · Motion In A Plane · NEET
No. Vector addition is commutative, so A + B = B + A. If you place B head-to-tail first and then A, you land on the exact same resultant R as when you place A first and then B. The two arrangements form the two halves of a parallelogram whose diagonal is the same R. Only the direction and length of the final resultant matter, not which vector you draw first.
It says (A + B) + C = A + (B + C). If you have three vectors, you can add A and B first and then add C, OR add B and C first and then add A. Both groupings give the identical resultant. This lets you regroup many vectors in whatever order is easiest, which is why we can freely rearrange terms like A + B + C + D when finding a net displacement.
No, they are different. Commutative is about ORDER of two vectors (swap them: A + B = B + A). Associative is about GROUPING of three or more vectors (change the brackets: (A + B) + C = A + (B + C)). NEET may test either idea, so keep them separate: order-swap = commutative, bracket-shift = associative.
No. Subtraction is NOT commutative: A - B is not equal to B - A. In fact B - A = -(A - B), so they point in opposite directions with the same magnitude. The commutative law holds only for addition, because A - B is really A + (-B), and the two negative terms fall on different sides.
When a body undergoes several displacements one after another, the total displacement is the vector sum of all of them. Because addition is commutative and associative, the net displacement depends only on the start and end points, not on the order in which the individual steps were taken. This is why we can add x-components and y-components separately in the analytical method.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For any two vectors A and B, A + B = B + A. The resultant is the same regardless of the order in which the two vectors are added.
For any three vectors A, B and C, (A + B) + C = A + (B + C). The resultant is the same regardless of how the vectors are grouped.
Yes. Ordinary numbers (scalars) are commutative and associative under addition (5 + 3 = 3 + 5). Vectors obey the same two laws, but with the extra rule that direction is also preserved in the resultant.
The dot product is commutative (A . B = B . A). The cross product is NOT commutative; A x B = -(B x A). This page is about vector ADDITION, which is always commutative.
Yes. Because addition is both commutative and associative, any number of vectors can be added in any order and any grouping. This is the basis of resolving each vector into components and adding all the x-parts and all the y-parts separately.
