Line through a point A parallel to a vector bबिंदु A से जाने वाली और सदिश b के समांतर रेखाPoint A se jaane wali aur vector b ke parallel line
NCERT Fig 11.3 · 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.
- Line l (रेखा l) — The line through A parallel to \vec{b}.
- Given point A (दिया गया बिंदु A) — Fixed point of the line; its position vector is \vec{a}.
- Any point P on the line (रेखा पर कोई बिंदु P) — P moves along the line as λ changes; its position vector is \vec{r}.
- Position vector \vec{a} = \overrightarrow{OA} (स्थिति सदिश \vec{a} = \overrightarrow{OA}) — Arrow from the origin to the given point A.
- Position vector \vec{r} = \overrightarrow{OP} (स्थिति सदिश \vec{r} = \overrightarrow{OP}) — Arrow from the origin to the moving point P.
- \overrightarrow{AP} = \lambda\vec{b} (\overrightarrow{AP} = \lambda\vec{b}) — \overrightarrow{AP} is parallel to \vec{b}, so it is a multiple \lambda\vec{b}; also \overrightarrow{AP} = \vec{r} - \vec{a}.
- Given vector \vec{b} (दिया गया सदिश \vec{b}) — Gives the direction of the line; its components are direction ratios.
- Vector equation of the line (रेखा का सदिश समीकरण) — \vec{r} = \vec{a} + \lambda\vec{b}: from \vec{r} - \vec{a} = \lambda\vec{b}.
Original diagram drawn by Simple Learning Hub, based on NCERT Fig 11.3. Report a mistake