Check sibling questions

Example 27 (Supplementary NCERT) - Show that a = i - 2j + 3k, b = -2i

Example 27 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

Example 27 (Supplementary NCERT) Show that the vectors π‘Ž βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚, 𝑏 βƒ— = βˆ’2𝑖 Μ‚ + 3𝑗 Μ‚ βˆ’ 4π‘˜ Μ‚ and 𝑐 βƒ— = 𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + 5π‘˜ Μ‚ are coplanarThree vectors π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— are coplanar if [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = 0 Given, 𝒂 βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚ 𝒃 βƒ— = βˆ’2𝑖 Μ‚ + 3𝑗 Μ‚ βˆ’ 4π‘˜ Μ‚ 𝒄 βƒ— = 𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + Ξ»π‘˜ Μ‚ [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = |β– 8(1&βˆ’2&[email protected]βˆ’2&3&βˆ’[email protected]&βˆ’3&5)| = 1[(3Γ—5)βˆ’(βˆ’3Γ—βˆ’4) ] βˆ’ (βˆ’2) [(βˆ’2Γ—5)βˆ’(1Γ—βˆ’4) ] + 3[(βˆ’2Γ—βˆ’3)βˆ’(1Γ—3) ] = 1 [15βˆ’(3 Γ—4)]+2[βˆ’10βˆ’(βˆ’4)]+3[(2 Γ—3)βˆ’3] = 1 [15βˆ’12]+2[βˆ’10+4]+3[6βˆ’3] = 1 [3]+2[βˆ’6]+3[3] = 3 – 12 + 9 = 0 Since [π‘Ž βƒ—" " 𝑏 βƒ—" " 𝑐 βƒ— ] = 0 Vectors 𝒂 βƒ—, 𝒃 βƒ—, 𝒄 βƒ— are coplanar

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.