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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 π‘Ž βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚, 𝑏 βƒ— = βˆ’2𝑖 Μ‚ + 3𝑗 Μ‚ βˆ’ 4π‘˜ Μ‚ and 𝑐 βƒ— = 𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + 5π‘˜ Μ‚ are coplanarThree vectors π‘Ž βƒ—, 𝑏 βƒ—, 𝑐 βƒ— are coplanar if [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = 0 Given, 𝒂 βƒ— = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 3π‘˜ Μ‚ 𝒃 βƒ— = βˆ’2𝑖 Μ‚ + 3𝑗 Μ‚ βˆ’ 4π‘˜ Μ‚ 𝒄 βƒ— = 𝑖 Μ‚ βˆ’ 3𝑗 Μ‚ + Ξ»π‘˜ Μ‚ [𝒂 βƒ—" " 𝒃 βƒ—" " 𝒄 βƒ— ] = |β– 8(1&βˆ’2&3@βˆ’2&3&βˆ’4@1&βˆ’3&5)| = 1[(3Γ—5)βˆ’(βˆ’3Γ—βˆ’4) ] βˆ’ (βˆ’2) [(βˆ’2Γ—5)βˆ’(1Γ—βˆ’4) ] + 3[(βˆ’2Γ—βˆ’3)βˆ’(1Γ—3) ] = 1 [15βˆ’(3 Γ—4)]+2[βˆ’10βˆ’(βˆ’4)]+3[(2 Γ—3)βˆ’3] = 1 [15βˆ’12]+2[βˆ’10+4]+3[6βˆ’3] = 1 [3]+2[βˆ’6]+3[3] = 3 – 12 + 9 = 0 Since [π‘Ž βƒ—" " 𝑏 βƒ—" " 𝑐 βƒ— ] = 0 Vectors 𝒂 βƒ—, 𝒃 βƒ—, 𝒄 βƒ— are coplanar

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