Ex 10.4, 1 - Find |a x b|, if a = i - 7j + 7k, b = 3i - 2j + 2k - Ex 10.4

Slide2.JPG

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

Transcript

Ex 10.4, 1 Find 𝑎﷯× 𝑏﷯﷯, if 𝑎﷯ = 𝑖﷯ − 7 𝑗﷯ + 7 𝑘﷯ and 𝑏﷯ = 3 𝑖﷯ − 2 𝑗﷯ + 2 𝑘﷯ 𝑎﷯ = 𝑖﷯ − 7 𝑗﷯ + 7 𝑘﷯ = 1 𝑖﷯ − 7 𝑗﷯ + 7 𝑘﷯ 𝑏﷯ = 3 𝑖﷯ − 2 𝑗﷯ + 2 k﷯ 𝑎﷯ × 𝑏﷯ = 𝑖﷯﷮ 𝑗﷯﷮ 𝑘﷯﷮ 1﷮3﷯﷮ −7﷮−2﷯﷮ 7﷮2﷯﷯﷯ = 𝑖﷯ −7﷮7﷮−2﷮2﷯﷯ − 𝑗﷯ 1﷮7﷮3﷮2﷯﷯ + k﷯ 1﷮−7﷮3﷮−2﷯﷯ = 𝑖﷯ −7 × 2 – (−2 × 7)﷯ − 𝑗﷯( 1×2 ﷯ − 3×7 ﷯) + 𝑘﷯( 1×2 ﷯ − (3 × −7)) = 𝑖﷯ −14− −14﷯﷯ − 𝑗﷯ 2−21 ﷯ + 𝑘﷯( −2−(−21)﷯ = 𝑖﷯ (0) − 𝑗﷯ (−19) + 𝑘﷯(19) = 0 𝑖﷯ + 19 𝑗﷯ + 19 𝑘﷯ ∴ 𝒂﷯ × 𝒃﷯ = 0 𝒊﷯ + 19 𝒋﷯ + 19 𝒌﷯ Magnitude of 𝑎﷯ × 𝑏﷯ = ﷮02+192+192﷯ 𝒂﷯ × 𝒃﷯﷯ = ﷮0+361+361﷯ = ﷮722﷯ = ﷮19×19×2 ﷯ = 19 ﷮𝟐﷯ Therefore, the magnitude of 𝑎﷯ × 𝑏﷯ is 19 ﷮𝟐﷯.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail