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Supplementary Exercise Q10 If the vectors 𝐴 ⃗ = a𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂, 𝐵 ⃗ = 𝑖 ̂ + b𝑗 ̂ + 𝑘 ̂ and 𝐶 ⃗ = 𝑖 ̂ + 𝑗 ̂ + c𝑘 ̂ are coplanar, then 1/(1âˆ’ğ‘Ž) + 1/(1−𝑏) + 1/(1−𝑐) = 1, where a, b, c ≠ 1 Since Vectors 𝐴 ⃗, 𝐵 ⃗, 𝐶 ⃗ are coplanar , ∴ [𝐴 ⃗" " 𝐵 ⃗" " 𝐶 ⃗ ] = 0 [𝐴 ⃗" " 𝐵 ⃗" " 𝐶 ⃗ ] = |■8(ğ‘Ž&1&1@1&𝑏&1@1&1&𝑐)| 0 = a[(𝑏×𝑐)−(1×1) ] − 1[(1×𝑐)−(1×1)] + 1[(1×1)−(1×𝑏) ] 0 = a [𝑏𝑐−1]−[𝑐−1]+1[1−𝑏] 0 = abc – a – c + 1 + 1 – b = 0

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.