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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&[email protected]&2&βˆ’[email protected]&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 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.