Supplementary Example 3

Last updated at Dec. 16, 2024 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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo