Scalar (dot) product of two vectorsदो सदिशों का अदिश (बिंदु) गुणनफल

NCERT Fig 5.1 · interactive diagram

Parts and their functions

• Vector A (सदिश A) — For work, A is the force F.
• Vector B (सदिश B) — For work, B is the displacement d.
• Angle θ between them (उनके बीच कोण θ) — θ < 90°: product positive; θ = 90°: zero; θ > 90°: negative.
• Projection B cos θ (प्रक्षेप B cos θ) — A · B = A × (projection of B on A). It is a scalar.
• Unit-vector rules (एकांक सदिशों के नियम) — Gives A · B = AₓBₓ + A_yB_y + A_zB_z. Example 5.1: F = 3î + 4ĵ − 5k̂, d = 5î + 4ĵ + 3k̂ ⇒ F·d = 16, cos θ = 16/50 = 0.32.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 5.1. Report a mistake