Adding vectors: triangle and parallelogram lawsसदिशों का योग: त्रिभुज और समांतर चतुर्भुज नियम

NCERT Fig 3.4 & 3.10 · interactive diagram

Parts and their functions

• Vector A (सदिश A) — Drawn first, from the origin.
• Vector B (tail at head of A) (सदिश B (पुच्छ, A के शीर्ष पर)) — Shift B parallel to itself so its tail sits on A’s head.
• Resultant R = A + B (परिणामी R = A + B) — Joins the tail of A to the head of B. Order does not matter: A + B = B + A.
• Side OP = A (भुजा OP = A) — Both vectors start from the same point O.
• Side OQ = B (भुजा OQ = B) — Completes the parallelogram OPSQ with A.
• Diagonal OS = R (विकर्ण OS = R) — R² = A² + B² + 2AB cos θ; tan α = B sin θ / (A + B cos θ), α measured from A.
• Angle θ between A and B (A और B के बीच कोण θ) — θ = 0 → R = A + B (maximum); θ = 180° → R = |A − B| (minimum); θ = 90° → R = √(A² + B²).

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 3.4 & 3.10. Report a mistake