1.4.3—A vector as two perpendicular components
- Syllabus
- 9702–2028–2029
- Objective
- 1.4.3
- Level
- AS
Perpendicular components reconstruct a vector’s magnitude and direction
Resolve a vector into perpendicular components Vx=Vcosθ and Vy=Vsinθ. Recover magnitude with √(Vx²+Vy²) and direction with a quadrant-aware tangent.
Choose axes before resolving, keep signs and use the angle measured from the correct axis. Components are not independent physical vectors unless the coordinate model says so.
A 10 N force at 30° above horizontal has components 10cos30° and 10sin30°.
Swapping sine and cosine changes which component is largest; the reference axis fixes the choice.
ConceptA-Level CAIE Physics AS