Position vector of P(x, y, z) and its componentsP(x, y, z) का स्थिति सदिश और उसके घटकP(x, y, z) ka position vector aur uske components
NCERT Fig 10.3 / 10.14 · Class 12 Maths · Chapter 10 · interactive diagram
Parts and what they mean
- Position vector \overrightarrow{OP} = \vec{r} (स्थिति सदिश \overrightarrow{OP} = \vec{r}) — The arrow from the origin O to P. Its length is \sqrt{x^2 + y^2 + z^2}.
- Point P(x, y, z) (बिंदु P(x, y, z)) — The tip of the position vector; its coordinates are the scalar components x, y, z.
- Origin O(0, 0, 0) (मूल बिंदु O(0, 0, 0)) — Every position vector starts here.
- Vector component x\hat{i} (सदिश घटक x\hat{i}) — Go x units along the x-axis: \overrightarrow{OQ} = x\hat{i}.
- Vector component y\hat{j} (सदिश घटक y\hat{j}) — Then y units parallel to the y-axis: \overrightarrow{QP_1} = y\hat{j}.
- Vector component z\hat{k} (सदिश घटक z\hat{k}) — Then z units up, parallel to the z-axis: \overrightarrow{P_1P} = z\hat{k}.
- Foot P_1 on the XY-plane (XY-तल पर पाद P_1) — The point below P on the XY-plane; |OP_1| = \sqrt{x^2 + y^2} (first use of Pythagoras).
- Segment OP_1 (रेखाखंड OP_1) — Shadow of OP on the floor (XY-plane). Then OP^2 = OP_1^2 + z^2 (second use of Pythagoras).
- Part of the XY-plane (XY-तल का भाग) — The "floor" z = 0.
- Direction angle γ (दिशा कोण γ) — The angle OP makes with the positive z-axis; \cos\gamma = \dfrac{z}{r} = n.
- x-axis (OX) (x-अक्ष (OX)) — Unit vector along it: \hat{i}.
- y-axis (OY) (y-अक्ष (OY)) — Unit vector along it: \hat{j}.
- z-axis (OZ) (z-अक्ष (OZ)) — Unit vector along it: \hat{k}.
- Component form (घटक रूप) — \vec{r} = x\hat{i} + y\hat{j} + z\hat{k}, |\vec{r}| = \sqrt{x^2 + y^2 + z^2}.
Original diagram drawn by Simple Learning Hub, based on NCERT Fig 10.3 / 10.14. Report a mistake