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  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co –terminus edges are (i) π‘Ž βƒ— = 2𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + 4π‘˜ Μ‚, 𝑏 βƒ— = 3𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + 2π‘˜ Μ‚, and 𝑐 βƒ— = 𝑖 Μ‚ + 2𝑗 Μ‚ βˆ’ π‘˜ Μ‚, Given, π‘Ž βƒ— = 2𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + 4π‘˜ Μ‚ , 𝑏 βƒ— = 3𝑖 Μ‚ – 𝑗 Μ‚ + 2π‘˜ Μ‚ , 𝑐 βƒ— = 𝑖 Μ‚ + 2𝑗 Μ‚ – π‘˜ Μ‚ Volume of parallelepiped = [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = |β– 8(2&βˆ’3&4@3&βˆ’1&2@1&2&βˆ’1)| = 2[(βˆ’1Γ—βˆ’1)βˆ’(2Γ—2) ] βˆ’ (βˆ’3) [(3Γ—βˆ’1)βˆ’(1Γ—2) ] + 4[(3Γ—2)βˆ’(1Γ—βˆ’1)] = 2 [1βˆ’4]+3(βˆ’3βˆ’2)+4[6+1] = 2(–3) + 3 (–5) + 4(7) = –6 – 15 + 28 = 7 Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co –terminus edges are (ii) π‘Ž βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚, 𝑏 βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ βˆ’ π‘˜ Μ‚, and 𝑐 βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ βˆ’ π‘˜ Μ‚, Given, π‘Ž βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚ , 𝑏 βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ – π‘˜ Μ‚ , 𝑐 βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ – π‘˜ Μ‚ Volume of parallelepiped = [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = |β– 8(1&βˆ’2&3@2&1&βˆ’1@2&1&βˆ’1)| = 1[(1Γ—βˆ’1)βˆ’(1Γ—βˆ’1)] βˆ’ (βˆ’2) [(2Γ—βˆ’1)βˆ’(2Γ—βˆ’1)] + 3[(2Γ—1)βˆ’(2Γ—1)] = 1 [βˆ’1+1]+2(βˆ’2+2)+3[2βˆ’2] = 1(0) + 2 (0) + 3(0) = 0

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.