VEC019 · Vectors · Classes 11–12
Vector applications
Forces add as vectors (parallelogram law). The resultant depends on both sizes and the angle between them.
RVector applications
📐 Formula
R = √(F₁² + F₂² + 2F₁F₂ cos θ)
✏️ Worked example
3 N and 4 N at 90°: R = √(9 + 16) = 5 N.
🌍 Where it is used
Towing, cranes, sailing against the wind, bridge design.
❓ Quick check
5 N and 5 N in opposite directions give…
🏋️ Practice
Easy6 N and 8 N at 90°?
Answer: 10 N
Medium2 N and 3 N in the same direction?
Answer: 5 N
ChallengeA boat at 4 m/s across a river flowing 3 m/s. Speed?
Answer: 5 m/s