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

Transcript

Supplementary Example 2 Find the volume of the parallelepiped whose edges are π‘Ž βƒ— = 2𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + 4π‘˜ Μ‚, 𝑏 βƒ— = 𝑖 Μ‚ + 2𝑗 Μ‚ βˆ’ π‘˜ Μ‚ and 𝑐 βƒ— = 2𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + 2π‘˜ Μ‚ Given, π‘Ž βƒ— = 2𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + 4π‘˜ Μ‚ , 𝑏 βƒ— = 𝑖 Μ‚ + 2𝑗 Μ‚ – π‘˜ Μ‚ , 𝑐 βƒ— = 2𝑖 Μ‚ – 𝑗 Μ‚ + 2π‘˜ Μ‚ Volume of parallelepiped = [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = |β– 8(2&βˆ’3&4@1&2&βˆ’1@2&βˆ’1&2)| = 2[(2Γ—2)βˆ’(βˆ’1Γ—βˆ’1) ] βˆ’ (βˆ’3) [(1Γ—2)βˆ’(2Γ—βˆ’1) ] + 4[(1Γ—βˆ’1)βˆ’(2Γ—2)] = 2 [4βˆ’1]+3(2+2)+4[βˆ’1βˆ’4] = 2(3) + 3 (4) + 4(–5) = 6 + 12 – 20 = –2 Since volume is always positive Volume of parallelepiped = 2 cubic units

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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.