Skew lines in a room: GE and DBकमरे में विषमतलीय रेखाएँ: GE और DBKamre mein skew lines: GE aur DB

NCERT Fig 11.5 · Class 12 Maths · Chapter 11 · interactive diagram

Parts and what they mean

• Room of size 1, 3, 2 units (1, 3, 2 इकाई माप का कमरा) — Along the x, y and z-axes respectively (NCERT Fig 11.5); O is a floor corner.
• Line GE (across the ceiling) (रेखा GE (छत पर तिरछी)) — From G(0, 0, 2) to E(1, 3, 2); direction \hat{i} + 3\hat{j}.
• Line DB (down the wall) (रेखा DB (दीवार पर नीचे)) — From D(1, 0, 2), the ceiling corner above A, to B(1, 3, 0); direction 3\hat{j} - 2\hat{k}.
• Shortest distance between GE and DB (GE और DB के बीच न्यूनतम दूरी) — The common perpendicular; by the formula of 11.5.1 its length is \dfrac{6}{7} unit. GE and DB are skew: not parallel and never meeting.
• O(0, 0, 0) (O(0, 0, 0)) — A corner of the room.
• A(1, 0, 0) (A(1, 0, 0)) — A corner of the room.
• B(1, 3, 0) (B(1, 3, 0)) — A corner of the room.
• C(0, 3, 0) (C(0, 3, 0)) — A corner of the room.
• D(1, 0, 2) (D(1, 0, 2)) — A corner of the room.
• E(1, 3, 2) (E(1, 3, 2)) — A corner of the room.
• F(0, 3, 2) (F(0, 3, 2)) — A corner of the room.
• G(0, 0, 2) (G(0, 0, 2)) — A corner of the room.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 11.5. Report a mistake