Example 27 (Supplementary NCERT) - Show that a = i - 2j + 3k, b = -2i

Example 27 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 27 (Supplementary NCERT) Show that the vectors 𝑎 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂, 𝑏 ⃗ = −2𝑖 ̂ + 3𝑗 ̂ − 4𝑘 ̂ and 𝑐 ⃗ = 𝑖 ̂ − 3𝑗 ̂ + 5𝑘 ̂ are coplanarThree vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = 0 Given, 𝒂 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂ 𝒃 ⃗ = −2𝑖 ̂ + 3𝑗 ̂ − 4𝑘 ̂ 𝒄 ⃗ = 𝑖 ̂ − 3𝑗 ̂ + λ𝑘 ̂ [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = |■8(1&−2&3@−2&3&−4@1&−3&5)| = 1[(3×5)−(−3×−4) ] − (−2) [(−2×5)−(1×−4) ] + 3[(−2×−3)−(1×3) ] = 1 [15−(3 ×4)]+2[−10−(−4)]+3[(2 ×3)−3] = 1 [15−12]+2[−10+4]+3[6−3] = 1 [3]+2[−6]+3[3] = 3 – 12 + 9 = 0 Since [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = 0 Vectors 𝒂 ⃗, 𝒃 ⃗, 𝒄 ⃗ are coplanar

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.