Angle between two linesदो रेखाओं के बीच का कोणDo lines ke beech ka angle

NCERT Fig 11.4 · 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_1 (direction ratios a_1, b_1, c_1) (रेखा L_1 (दिक्-अनुपात a_1, b_1, c_1)) — Drawn with direction \vec{b_1} = \hat{i} + 2\hat{j} + 2\hat{k} of NCERT Example 7.
• Line L_2 (direction ratios a_2, b_2, c_2) (रेखा L_2 (दिक्-अनुपात a_2, b_2, c_2)) — Drawn with direction \vec{b_2} = 3\hat{i} + 2\hat{j} + 6\hat{k} of NCERT Example 7.
• Point P on L_1 (L_1 पर बिंदु P) — \overrightarrow{OP} is a vector with components a_1, b_1, c_1.
• Point Q on L_2 (L_2 पर बिंदु Q) — \overrightarrow{OQ} is a vector with components a_2, b_2, c_2.
• Acute angle θ (न्यून कोण θ) — For Example 7, \cos\theta = \dfrac{19}{21}, so θ is about 25.2°.
• Angle formula (कोण का सूत्र) — \cos\theta = \dfrac{|\vec{b_1}\cdot\vec{b_2}|}{|\vec{b_1}||\vec{b_2}|} — only the directions are used.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 11.4. Report a mistake