Vectors — Mathematics, 14–17
A vector describes both a size and a direction. It gives a precise way to combine movements, forces and changes without losing the difference between going north and going south.
Size and direction together
A number can tell how far or how strongly, but not where. A vector carries both pieces of information, such as 4 metres east or a force of 10 newtons upward. In coordinates, its components record the horizontal and vertical parts.
Why vectors were needed
Scientists and engineers needed a language for quantities that do not behave like ordinary totals. Two journeys of 5 km can cancel if they point in opposite directions, while two forces can combine into one result. Vectors keep direction visible during these calculations.
Adding two movements
A robot moves 3 m east, then 4 m north. Write the movements as (3, 0) and (0, 4), then add components: (3, 0) + (0, 4) = (3, 4). Its straight-line distance from the start is √(3² + 4²) = 5 m, although it travelled 7 m.
Distance is not displacement
It is tempting to add every distance travelled and call the answer the final movement. That is reasonable when direction is irrelevant, but a vector describes the start-to-finish change: walking 10 m east and 10 m west gives 20 m travelled, yet a zero displacement.
Vectors in motion and design
Navigation apps combine your movement with a vehicle’s movement to predict a route. In games and animation, vectors control an object’s position, speed and direction. Engineers also use them to combine forces on bridges, aircraft and machines.
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