Projection of a on bb पर a का प्रक्षेपb par a ka projection

NCERT Fig 10.20 · Class 12 Maths · Chapter 10 · interactive diagram

Parts and what they mean

• Vector \vec{a} (सदिश \vec{a}) — The vector whose shadow we want.
• Vector \vec{b} (the line we project on) (सदिश \vec{b} (जिस पर प्रक्षेप लेते हैं)) — Only its direction matters: use \hat{b} = \dfrac{\vec{b}}{|\vec{b}|}.
• Angle θ between \vec{a} and \vec{b} (\vec{a} और \vec{b} के बीच कोण θ) — If θ is obtuse, the foot falls behind O and the projection is negative.
• Perpendicular from the tip of \vec{a} (\vec{a} के सिरे से लंब) — Drop it onto the line of \vec{b} — like light falling straight down.
• Projection = |\vec{a}|\cos\theta = \vec{a} \cdot \hat{b} (प्रक्षेप = |\vec{a}|\cos\theta = \vec{a} \cdot \hat{b}) — The signed length OM; equals \dfrac{\vec{a} \cdot \vec{b}}{|\vec{b}|}. The projection vector is \overrightarrow{OM} = (\vec{a} \cdot \hat{b})\,\hat{b}.
• Common tail O (उभयनिष्ठ पूँछ O) — Put both vectors tail to tail to read θ.
• Foot of perpendicular M (लंब का पाद M) — OM is the projection.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 10.20. Report a mistake