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Supplementary Example 3 - Show vectors a, b, c are coplanar - Supplementary examples and questions from CBSE

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Supplementary Example 3 Show that the vectors 𝑎﷯ = −4 𝑖﷯ − 6 𝑗﷯ − 2 𝑘﷯, 𝑏﷯ = − 𝑖﷯ + 4 𝑗﷯ + 3 𝑘﷯ and 𝑐﷯ = −8 𝑖﷯ − 𝑗﷯ + 3 𝑘﷯ are coplanar Three vectors 𝑎﷯, 𝑏﷯, 𝑐﷯ are coplanar if 𝒂﷯ 𝒃﷯ 𝒄﷯﷯ = 0 Given, 𝑎﷯ = –4 𝑖﷯ − 6 𝑗﷯ – 2 𝑘﷯ 𝑏﷯ = − 𝑖﷯ + 4 𝑗﷯ + 3 𝑘﷯ 𝑐﷯ = –8 𝑖﷯ − 𝑗﷯ + 3 𝑘﷯ 𝑎﷯ 𝑏﷯ 𝑐﷯﷯ = −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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