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Supplementary Q6 - Prove i.(k x j) = j.(ixk) = k.(jxi) = -1 - Supplementary examples and questions from CBSE

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Supplementary Exercise Q6 if 𝑖﷯, 𝑗﷯ and 𝑘﷯ are three mutually perpendicular vectors, prove that 𝑖﷯. 𝑘﷯× 𝑗﷯﷯ = 𝑗﷯. 𝑖﷯× 𝑘﷯﷯ = 𝑘﷯.( 𝑗﷯ × 𝑖﷯) = −1 Here, 𝑖﷯ = 1 𝑖﷯ + 0 𝑗﷯ + 0 𝑘﷯ 𝑗﷯ = 0 𝑖﷯ + 1 𝑗﷯ + 0 𝑘﷯ 𝑘﷯ = 0 𝑖﷯ + 0 𝑗﷯ + 1 𝑘﷯ 𝒊﷯. 𝒌﷯× 𝒋﷯﷯ = 𝑖﷯﷮ 𝑘﷯﷮ 𝑗﷯﷯﷯ = 1﷮0﷮0﷮0﷮0﷮1﷮0﷮1﷮0﷯﷯ = 1(0 – 1) – 0(0 – 0) + 0(0 – 0) = –1 𝒋﷯. 𝒊﷯× 𝒌﷯﷯ = 𝑗﷯﷮ 𝑖﷯﷮𝑘﷯﷯ = 0﷮1﷮0﷮1﷮0﷮0﷮0﷮0﷮1﷯﷯ = 0(0 – 0) – 1(1 – 0) + 0(0 – 0) = –1 𝒌﷯. 𝒋﷯× 𝒊﷯﷯ = 𝑘﷯﷮ 𝑗﷯﷮ 𝑖﷯﷯﷯ = 0﷮0﷮1﷮0﷮1﷮0﷮1﷮0﷮0﷯﷯ = 0(0 – 0) – 0(0 – 0) + 1(0 – 1) = –1

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