Vector Operation Explorer

Build two vectors by components, add or subtract them geometrically, scale vector A, and connect the resultant to magnitude, direction and dot product.

Model presets

Reviewed starting states

Vector A · x 3

Vector A · y 4

Vector B · x -1

Vector B · y 2

Scale factor k 2

Resultant x-component: 2.00
Resultant y-component: 6.00
Resultant magnitude: 6.32
Resultant direction: 71.6 °
A · B: 5.00
Angle between A and B: 63.4 °
Magnitude of A: 5.00
Magnitude of B: 2.24

Curriculum map

AQA GCSE Mathematics
Geometry and Measures → Vector arithmetic and geometric proof
Edexcel A-Level Mathematics
Vectors → Magnitude, direction and scalar product
OCR A-Level Physics
Foundations of Physics → Resolving and combining vectors

Model boundaries

All vectors are two-dimensional Cartesian vectors on a common coordinate scale.
Direction is measured anticlockwise from the positive x-axis and may be negative below that axis.
The angle between vectors is reported as zero when either vector has zero magnitude because its direction is undefined.

StudyVector-authored vector model using standard component arithmetic, Euclidean magnitude and scalar-product relationships; mapped to the reviewed topics shown below.

Accessible text description

A square Cartesian grid shows vector A in cyan, vector B in violet and the selected resultant in orange. Addition and subtraction include a dashed head-to-tail construction; scaling shows kA from the origin. Component labels, magnitudes, direction, dot product and angle are repeated in formula cards and the measurement panel. Native plus and minus buttons adjust every component.

Model presets

Live measurements

Curriculum map

Model boundaries