web analytics

Supplementary Exercise Q3  - Find volumes of parallelepipeds - Supplementary examples and questions from CBSE

Slide22.JPG

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
Ask Download

Transcript

Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co –terminus edges are (i) 𝑎﷯ = 2 𝑖﷯ − 3 𝑗﷯ + 4 𝑘﷯, 𝑏﷯ = 3 𝑖﷯ − 𝑗﷯ + 2 𝑘﷯, and 𝑐﷯ = 𝑖﷯ + 2 𝑗﷯ − 𝑘﷯, Given, 𝑎﷯ = 2 𝑖﷯ − 3 𝑗﷯ + 4 𝑘﷯ , 𝑏﷯ = 3 𝑖﷯ – 𝑗﷯ + 2 𝑘﷯ , 𝑐﷯ = 𝑖﷯ + 2 𝑗﷯ – 𝑘﷯ Volume of parallelepiped = 𝒂﷯ 𝒃﷯ 𝒄﷯﷯ = 2﷮−3﷮4﷮3﷮−1﷮2﷮1﷮2﷮−1﷯﷯ = 2 −1×−1﷯−(2×2) ﷯ − (−3) 3×−1﷯−(1×2) ﷯ + 4 3×2﷯−(1×−1)﷯ = 2 1−4﷯+3 −3−2﷯+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) 𝑎﷯ = 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯, 𝑏﷯ = 2 𝑖﷯ + 𝑗﷯ − 𝑘﷯, and 𝑐﷯ = 2 𝑖﷯ + 𝑗﷯ − 𝑘﷯, Given, 𝑎﷯ = 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯ , 𝑏﷯ = 2 𝑖﷯ + 𝑗﷯ – 𝑘﷯ , 𝑐﷯ = 2 𝑖﷯ + 𝑗﷯ – 𝑘﷯ Volume of parallelepiped = 𝒂﷯ 𝒃﷯ 𝒄﷯﷯ = 1﷮−2﷮3﷮2﷮1﷮−1﷮2﷮1﷮−1﷯﷯ = 1 1×−1﷯−(1×−1)﷯ − (−2) 2×−1﷯−(2×−1)﷯ + 3 2×1﷯−(2×1)﷯ = 1 −1+1﷯+2 −2+2﷯+3 2−2﷯ = 1(0) + 2 (0) + 3(0) = 0

About the Author

CA Maninder Singh's photo - Expert in Practical Accounts, Taxation and Efiling
CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .
Jail