Distance between two parallel linesदो समांतर रेखाओं के बीच की दूरीDo parallel lines ke beech ki distance

NCERT Fig 11.7 · Class 12 Maths · Chapter 11 · interactive diagram

Parts and what they mean

• Line l_1: \vec{r} = \vec{a_1} + \lambda\vec{b} (रेखा l_1: \vec{r} = \vec{a_1} + \lambda\vec{b}) — First line; S on it has position vector \vec{a_1}.
• Line l_2: \vec{r} = \vec{a_2} + \mu\vec{b} (रेखा l_2: \vec{r} = \vec{a_2} + \mu\vec{b}) — Same direction \vec{b}, so parallel to l_1; the two lines are coplanar.
• S (position vector \vec{a_1}) (S (स्थिति सदिश \vec{a_1})) — Known point on l_1.
• T (position vector \vec{a_2}) (T (स्थिति सदिश \vec{a_2})) — Known point on l_2.
• P — foot of the perpendicular from T on l_1 (P — T से l_1 पर लंब का पाद) — TP is perpendicular to l_1.
• \overrightarrow{ST} = \vec{a_2} - \vec{a_1} (\overrightarrow{ST} = \vec{a_2} - \vec{a_1}) — Joins the two known points.
• Distance d = TP (दूरी d = TP) — d = \dfrac{|\vec{b}\times(\vec{a_2} - \vec{a_1})|}{|\vec{b}|}, because TP = ST\sin\theta.
• Common direction \vec{b} (उभयनिष्ठ दिशा \vec{b}) — Both lines are parallel to \vec{b}.
• θ — angle between \vec{b} and \overrightarrow{ST} (θ — \vec{b} और \overrightarrow{ST} के बीच कोण) — |\vec{b}\times\overrightarrow{ST}| = |\vec{b}|\,ST\sin\theta = |\vec{b}|\,TP.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 11.7. Report a mistake