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

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

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.