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Supplementary examples and questions from CBSE
Supplementary Example 2 Important Deleted for CBSE Board 2024 Exams
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Supplementary Exercise Q1 Deleted for CBSE Board 2024 Exams
Supplementary Exercise Q2 Deleted for CBSE Board 2024 Exams
Supplementary Exercise Q3 Deleted for CBSE Board 2024 Exams
Supplementary Exercise Q4 Important Deleted for CBSE Board 2024 Exams
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Supplementary examples and questions from CBSE
Last updated at May 29, 2023 by Teachoo
Supplementary Exercise Q5 Find the value of 𝜆 if the following vectors are co-planar (i) 𝑎 ⃗ = 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂, 𝑏 ⃗ = 𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂, and 𝑐 ⃗ = 3𝑖 ̂ − 𝜆𝑗 ̂ + 5𝑘 ̂ Three vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = 0 Given, 𝑎 ⃗ = 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ 𝑏 ⃗ = 𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂ 𝑐 ⃗ = 3𝑖 ̂ − λ 𝑗 ̂ + 5𝑘 ̂ [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = |■8(2&−1&[email protected]&2&−[email protected]&−𝜆&5)| 0 = 2[(2×5)−(−λ×−3) ] − (−1) [(1×5)−(3×−3) ] + 1[(1×−λ)−(3×2) ] 0 = 2[10−3λ] + [5+9 ] + [−λ−6] 0 = 20 – 6λ + 14 – λ +– 6 0 = –7λ + 28 7λ = 28 λ = 28/7 𝝀 = 4 Therefore, 𝑎 ⃗,𝑏,𝑐 ⃗ are coplanar if λ = 4 Supplementary Exercise Q5 Find the value of 𝜆 if the following vectors are co-planar (ii) 𝑎 ⃗ = 2𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂, 𝑏 ⃗ = 2𝑖 ̂ − 𝜆𝑗 ̂ + 𝑘 ̂, and 𝑐 ⃗ = 5𝑖 ̂ − 𝑗 ̂ − 3𝑘 ̂ Three vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = 0 Given, 𝑎 ⃗ = 2𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂ 𝑏 ⃗ = 2𝑖 ̂ − λ𝑗 ̂ + 𝑘 ̂ 𝑐 ⃗ = 5𝑖 ̂ + 𝑗 ̂ – 3𝑘 ̂ [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = |■8(2&1&[email protected]&−𝜆&[email protected]&1&−3)| 0 = 2[(−λ×−3)−(1×1)] − 1[(2×−3)−(5×1)] + 1[(2×1)−(5×−λ) ] 0 = 2[3λ−1] − 1[−6−5] + 1[2+5λ] 0 = 6λ – 2 + 11 + 2 + 5λ 0 = 11λ + 11 –11λ = 11 λ = 11/(−11) 𝝀 = –1 Therefore, 𝑎 ⃗,𝑏,𝑐 ⃗ are coplanar if λ = –1