Section formula: R divides PQ in m : nखंड सूत्र: R, PQ को m : n में विभाजित करता हैSection formula: R, PQ ko m : n mein divide karta hai

NCERT Fig 10.16 · Class 12 Maths · Chapter 10 · interactive diagram

Parts and what they mean

• Position vector \vec{a} = \overrightarrow{OP} (स्थिति सदिश \vec{a} = \overrightarrow{OP}) — Where P is, seen from O.
• Position vector \vec{b} = \overrightarrow{OQ} (स्थिति सदिश \vec{b} = \overrightarrow{OQ}) — Where Q is, seen from O.
• Position vector \vec{r} = \overrightarrow{OR} (स्थिति सदिश \vec{r} = \overrightarrow{OR}) — From m\,\overrightarrow{RQ} = n\,\overrightarrow{PR}: m(\vec{b} - \vec{r}) = n(\vec{r} - \vec{a}), so \vec{r} = \dfrac{m\vec{b} + n\vec{a}}{m + n}.
• Point R (here m : n = 2 : 1) (बिंदु R (यहाँ m : n = 2 : 1)) — R is closer to the end with the smaller share: PR : RQ = m : n.
• Ratio m : n (अनुपात m : n) — m is the part next to P, n the part next to Q. In the formula, m goes with \vec{b} (the far end) — the cross pattern.
• Segment PQ (रेखाखंड PQ) — For external division R lies on PQ extended and \vec{r} = \dfrac{m\vec{b} - n\vec{a}}{m - n}.
• Origin O (मूल बिंदु O) — All three position vectors start here.
• Point P (बिंदु P) — End with position vector \vec{a}.
• Point Q (बिंदु Q) — End with position vector \vec{b}.
• Section formula (internal) (खंड सूत्र (अंतः)) — Mid-point (m = n): \vec{r} = \dfrac{\vec{a} + \vec{b}}{2}.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 10.16. Report a mistake