Ex 10.5, 2 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra

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Ex 10.5, 2 (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) ]