Example 28 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra

Last updated at Dec. 16, 2024 by Teachoo

Example 28 (Supplementary NCERT) - Find lambda if a = i + 3j +k, b = 2

Example 28 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2

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Transcript

Example 28 (Supplementary NCERT) Find 𝜆 if the vectors 𝑎 ⃗ = 𝑖 ̂ + 3𝑗 ̂ + 𝑘 ̂, 𝑏 ⃗ = 2𝑖 ̂ – 𝑗 ̂ − 𝑘 ̂ and 𝑐 ⃗ = 𝜆𝑖 ̂ + 7𝑗 ̂ + 3𝑘 ̂ are coplanar.Three vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = 0 Given, 𝒂 ⃗ = 𝑖 ̂ + 3𝑗 ̂ + 𝑘 ̂ 𝒃 ⃗ = 2𝑖 ̂ – 𝑗 ̂ − 𝑘 ̂ 𝒄 ⃗ = λ𝑖 ̂ + 7𝑗 ̂ + 3𝑘 ̂ [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = |■8(1&3&1@2&−1&−1@𝜆&7&3)| 0 = 1[(−1×3)−(7×−1) ] − 3[(2×3)−(λ×−1) ] + 1[(2×7)−(λ×−1) ] 0 = 1 [−3−(−7)]−3[6−(−λ)]+1[14−(−λ)] 0 = 1 [−3+7]−3[6+λ]+1[14+λ] 0 = 4 – 18 – 3λ + 14 + λ 0 = 18 – 18 – 3λ + λ 0 = – 2λ –2λ = 0 λ = 0/(−2) 𝝀 = 0 Therefore, 𝑎 ⃗,𝑏,𝑐 ⃗ are coplanar if λ = 0

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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 and Computer Science at Teachoo

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