Vector field introduction

A vector field attaches a vector to every point: wind maps, water currents, magnetic fields. F(x, y) = (−y, x) swirls around the origin; F = (x, y) spreads outwards.

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📐 Formula

F(x, y) = (P(x, y), Q(x, y))

✏️ Worked example

In F = (−y, x), at (2, 1) the arrow is (−1, 2), of strength √5 ≈ 2.24.

🌍 Where it is used

Weather maps, fluid flow, electromagnetism.

❓ Quick check

In F = (x, y), arrows point…

🏋️ Practice

EasyF = (−y, x) at (0, 3)?

Answer: (−3, 0)

MediumF = (x, y) at (1, −2)?

Answer: (1, −2)

ChallengeWhere is F = (x, y) zero?

Answer: At the origin