Vectors

Connect the arrows, the coordinates and the geometry.

Start with the arithmetic or choose the question you need help with. Change components, compare directions and move the models yourself. Written explanations and solutions stay available independently of the animations.

Vector arithmeticAdd and subtract vectors, multiply by a scalar and work with column vectors and i/j notation. Connect component calculations to head-to-tail diagrams.
Vector magnitude and directionFind vector lengths, unit vectors and directions with the correct quadrant. Resolve components, find angles between vectors and calculate triangle or parallelogram areas.
Position vectorsUse end minus start to find displacements and distances. Recover endpoints, find possible parallelogram vertices and solve position constraints involving lines and circles.
Vector geometryDivide lines in a ratio and use vectors to prove parallelism, collinearity and geometric results. Includes midpoint theorems, intersections, regular hexagons and diagonal ratios.
Velocity, displacement and force vectorsSolve vector problems involving speed, displacement, bearings, travel time, acceleration and resultant forces. Check units, direction and modelling assumptions.

Useful foundations

Review coordinate geometry, the cosine rule or simultaneous equations when those steps need a refresher.