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Supplementary Example 3

Last updated at May 29, 2023 by

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Supplementary Example 3 Show that the vectors 𝑎 ⃗ = −4𝑖 ̂ − 6𝑗 ̂ − 2𝑘 ̂, 𝑏 ⃗ = −𝑖 ̂ + 4𝑗 ̂ + 3𝑘 ̂ and 𝑐 ⃗ = −8𝑖 ̂ − 𝑗 ̂ + 3𝑘 ̂ are coplanar Three vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = 0 Given, 𝑎 ⃗ = –4𝑖 ̂ − 6𝑗 ̂ – 2𝑘 ̂ 𝑏 ⃗ = −𝑖 ̂ + 4𝑗 ̂ + 3𝑘 ̂ 𝑐 ⃗ = –8𝑖 ̂ − 𝑗 ̂ + 3𝑘 ̂ [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = |■8(−4&−6&−2@−1&4&3@−8&−1&3)| = –4[(4×3)−(−1×3) ] − (−6) [(−1×3)−(−8×3) ] + (–2)[(−1×−1)−(−8×4)] = –4 [12+3]+6(−3+24)−2[1+32] = –4(15) + 6 (21) –2(33) = –60 + 126 – 66 = 0 Since [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = 0 Vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar

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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.