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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 ̂ = 1𝑖 ̂ + 0𝑗 ̂ + 0𝑘 ̂ 𝑗 ̂ = 0𝑖 ̂ + 1𝑗 ̂ + 0𝑘 ̂ 𝑘 ̂ = 0𝑖 ̂ + 0𝑗 ̂ + 1𝑘 ̂ 𝒊 ̂.(𝒌 ̂×𝒋 ̂ ) = [■8(𝑖 ̂&𝑘 ̂&𝑗 ̂ )] = [■8(1&0&[email protected]&0&[email protected]&1&0)] = 1(0 – 1) – 0(0 – 0) + 0(0 – 0) = –1 𝒋 ̂.(𝒊 ̂×𝒌 ̂ ) = [■8(𝑗 ̂&𝑖 ̂&𝑘)] = [■8(0&1&[email protected]&0&[email protected]&0&1)] = 0(0 – 0) – 1(1 – 0) + 0(0 – 0) = –1 𝒌 ̂.(𝒋 ̂×𝒊 ̂ ) = [■8(𝑘 ̂&𝑗 ̂&𝑖 ̂ )] = [■8(0&0&[email protected]&1&[email protected]&0&0)] = 0(0 – 0) – 0(0 – 0) + 1(0 – 1) = –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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.