Direction angles and direction cosines of a lineरेखा के दिक्-कोण और दिक्-कोसाइनLine ke direction angles aur direction cosines

NCERT Fig 11.1 · Class 12 Maths · Chapter 11 · interactive diagram

Parts and what they mean

• x-axis (OX) (x-अक्ष (OX)) — One of the three mutually perpendicular axes; here it comes out of the page towards you.
• y-axis (OY) (y-अक्ष (OY)) — The second axis, drawn to the right.
• z-axis (OZ) (z-अक्ष (OZ)) — The third axis, pointing straight up.
• Origin O(0, 0, 0) (मूल बिंदु O(0, 0, 0)) — The point where the three axes meet.
• Directed line L (दिष्ट रेखा L) — A line through O with a chosen direction (the arrow).
• Point P on L (L पर बिंदु P) — Any point of the line; OP points in the direction of L.
• Direction angle α (दिक्-कोण α) — Angle between L and the positive x-axis; l = \cos\alpha.
• Direction angle β (दिक्-कोण β) — Angle between L and the positive y-axis; m = \cos\beta.
• Direction angle γ (दिक्-कोण γ) — Angle between L and the positive z-axis; n = \cos\gamma.
• Reversed direction (उलटी दिशा) — Taking the line the other way gives angles \pi-\alpha, \pi-\beta, \pi-\gamma and direction cosines -l, -m, -n.
• Direction cosines (दिक्-कोसाइन) — The cosines of the three direction angles; always l^2+m^2+n^2=1.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 11.1. Report a mistake