Parallelogram law of vector additionसदिश योग का समांतर चतुर्भुज नियमParallelogram law of vector addition

NCERT Fig 10.9 · Class 12 Maths · Chapter 10 · interactive diagram

Parts and what they mean

• Vector \vec{a} = \overrightarrow{OA} (सदिश \vec{a} = \overrightarrow{OA}) — One adjacent side.
• Vector \vec{b} = \overrightarrow{OC} (सदिश \vec{b} = \overrightarrow{OC}) — The other adjacent side, from the same point O (coinitial).
• Diagonal \overrightarrow{OB} = \vec{a} + \vec{b} (विकर्ण \overrightarrow{OB} = \vec{a} + \vec{b}) — The diagonal through the common point O is the sum: parallelogram law.
• Side \overrightarrow{AB} = \vec{b} (भुजा \overrightarrow{AB} = \vec{b}) — Opposite sides are equal and parallel, so \overrightarrow{AB} = \overrightarrow{OC}; then OA + AB = OB is the triangle law.
• Side \overrightarrow{CB} = \vec{a} (भुजा \overrightarrow{CB} = \vec{a}) — Route O → C → B gives \vec{b} + \vec{a}, the same diagonal: \vec{a} + \vec{b} = \vec{b} + \vec{a}.
• Parallelogram OABC (समांतर चतुर्भुज OABC) — Built on \vec{a} and \vec{b} as adjacent sides.
• Common point O (उभयनिष्ठ बिंदु O) — Both vectors start here.
• Vertex A (शीर्ष A) — Head of \vec{a}.
• Vertex B (शीर्ष B) — Head of the resultant \vec{a} + \vec{b}.
• Vertex C (शीर्ष C) — Head of \vec{b}.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 10.9. Report a mistake