Misc 18 - The value of i.(j x k) + j.(i x k) + k.(i x j) is

Misc 18 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Misc 18 (Introduction) The value of 𝑖 Μ‚.(𝑗 Μ‚ Γ— π‘˜ Μ‚) + 𝑗 Μ‚. (𝑖 Μ‚ Γ— π‘˜ Μ‚) + π‘˜ Μ‚.(𝑖 Μ‚ Γ— 𝑗 Μ‚) (A) 0 (B) βˆ’1 (C) 1 (D) 3 π’Š Μ‚ Γ— 𝒋 Μ‚ = π‘˜ Μ‚ 𝒋 Μ‚ Γ— π’Œ Μ‚ = 𝑖 Μ‚ π’Œ Μ‚ Γ— π’Š Μ‚ = 𝑗 Μ‚ 𝒋 Μ‚ Γ— π’Š Μ‚ = β€“π‘˜ Μ‚ π’Œ Μ‚ Γ— 𝒋 Μ‚ = βˆ’π‘– Μ‚ π’Š Μ‚ Γ— π’Œ Μ‚ = βˆ’π‘— Μ‚ Misc 18 The value of 𝑖 Μ‚.(𝑗 Μ‚ Γ— π‘˜ Μ‚) + 𝑗 Μ‚. (𝑖 Μ‚ Γ— π‘˜ Μ‚) + π‘˜ Μ‚.(𝑖 Μ‚ Γ— 𝑗 Μ‚) (A) 0 (B) βˆ’1 (C) 1 (D) 3 Now, 𝑖 Μ‚.(𝑗 Μ‚ Γ— π‘˜ Μ‚) + 𝑗 Μ‚. (𝑖 Μ‚ Γ— π‘˜ Μ‚) + π‘˜ Μ‚.(𝑖 Μ‚ Γ— 𝑗 Μ‚) = 𝑖 Μ‚.(π’Š Μ‚) + 𝑗 Μ‚.(βˆ’π’‹ Μ‚) + π‘˜ Μ‚ .(π’Œ Μ‚) = 𝑖 Μ‚. 𝑖 Μ‚ βˆ’ 𝑗 Μ‚ . 𝑗 Μ‚ + π‘˜ Μ‚. π‘˜ Μ‚ = 1 – 1 + 1 = 1 So, option C is correct 𝑖 Μ‚. 𝑖 Μ‚ = |𝑖 Μ‚ ||𝑖 Μ‚ | cos 0 = 1 Γ— 1 Γ— 1 = 1 Similarly, 𝑗 Μ‚ . 𝑗 Μ‚ = π‘˜ Μ‚ . π‘˜ Μ‚ = 1

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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.