Misc 18 - Value of i.(j x k) + j.(i x k) + k.(i x j) - Miscellaneous

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Misc 18 (Introduction) The value of 𝑖﷯.( 𝑗﷯ × 𝑘﷯) + 𝑗﷯. ( 𝑖﷯ × 𝑘﷯) + 𝑘﷯.( 𝑖﷯ × 𝑗﷯) (A) 0 (B) −1 (C) 1 (D) 3 Misc 18 The value of 𝑖﷯.( 𝑗﷯ × 𝑘﷯) + 𝑗﷯. ( 𝑖﷯ × 𝑘﷯) + 𝑘﷯.( 𝑖﷯ × 𝑗﷯) (A) 0 (B) −1 (C) 1 (D) 3 Now, 𝑖﷯.( 𝑗﷯ × 𝑘﷯) + 𝑗﷯. ( 𝑖﷯ × 𝑘﷯) + 𝑘﷯.( 𝑖﷯ × 𝑗﷯) = 𝑖﷯.( 𝒊﷯) + 𝑗﷯.(− 𝒋﷯) + 𝑘﷯ .( 𝒌﷯) = 𝑖﷯. 𝑖﷯ − 𝑗﷯ . 𝑗﷯ + 𝑘﷯. 𝑘﷯ = 1 – 1 + 1 = 1 So, option C is correct

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