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Vector Generator

Generates a random 2D vector with whole-number components from -20 to 20, drawn independently on each axis, and computes its magnitude from them — for vector-maths teaching, magnitude-practice worksheets, or placeholder data for physics and graphics demos that need a vector rather than a bare pair of numbers.

What this generator does

Produces a vector of random components, for maths practice and for filling geometry or physics test cases.

How to use this tool

  1. Press generate for a random vector.

Worked examples

Format
(-12, 12) |v| = 16.97 and (19, -12) |v| = 22.47 — two consecutive draws

Common use cases

  • Vector-maths teaching examples
  • Placeholder data for physics or graphics demos
  • Quick vector-magnitude practice

How this generator works

Two whole-number components are each drawn independently from −20 to 20, and the magnitude is computed from them as the square root of the sum of their squares, rounded to two decimal places. Drawing the components rather than a magnitude and a direction gives points uniformly distributed in a square, which is right for test data and wrong for a random direction — direction needs a different construction, and doing it this way clusters directions towards the corners.

Limitations and good to know

  • Two dimensions and a −20 to 20 range are fixed; there is no control for a third component or for wider bounds.
  • Components are drawn independently, so the vector is not normalised and its direction is not uniformly distributed round the circle.
  • The magnitude is derived and rounded for display, so recomputing it from the shown components can differ in the last place.
  • No units and no coordinate convention are implied.
  • The zero vector (0, 0) can be drawn — one press in 1,681 — and it has no direction at all; normalising it divides by zero.

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