Supplementary Exercise Q10
Last updated at April 16, 2024 by Teachoo
Supplementary examples and questions from CBSE
Supplementary examples and questions from CBSE
Last updated at April 16, 2024 by Teachoo
Supplementary Exercise Q10 If the vectors 𝐴 ⃗ = a𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂, 𝐵 ⃗ = 𝑖 ̂ + b𝑗 ̂ + 𝑘 ̂ and 𝐶 ⃗ = 𝑖 ̂ + 𝑗 ̂ + c𝑘 ̂ are coplanar, then 1/(1−𝑎) + 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(𝑎&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