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Add vectors component by component: (a₁+b₁, a₂+b₂[, a₃+b₃]). Geometrically the head-to-tail resultant — forces, velocities, displacements.
Component-wise resultant of two 2D/3D vectors.
u + v = (u₁+v₁, u₂+v₂[, u₃+v₃])
| Symbol | Meaning |
|---|---|
| u + v | Resultant vector |
(1,2) + (3,−1) = (4,1). In 3D: (1,2,3) + (4,5,6) = (5,7,9).
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Place v's tail at u's head; the resultant runs from u's tail to v's head.
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Content updated: September 2026