Show that (i) the vectors a = 2i - j + k, b = i + 2j - 3k and c = 3i - - Supplementary examples and questions from CBSE

part 2 - Supplementary Exercise Q4 - Supplementary examples and questions from CBSE - Serial order wise - Chapter 10 Class 12 Vector Algebra
part 3 - Supplementary Exercise Q4 - Supplementary examples and questions from CBSE - Serial order wise - Chapter 10 Class 12 Vector Algebra
part 4 - Supplementary Exercise Q4 - Supplementary examples and questions from CBSE - Serial order wise - Chapter 10 Class 12 Vector Algebra

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Supplementary Exercise Q4 Show that (i) the vectors 𝑎 ⃗ = 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂, 𝑏 ⃗ = 𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂, and 𝑐 ⃗ = 3𝑖 ̂ − 4𝑗 ̂ + 5𝑘 ̂ are coplanar. Three vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [ 𝒂 ⃗, 𝒃 ⃗, 𝒄 ⃗ ] = 0 Given, 𝑎 ⃗ = 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ 𝑏 ⃗ = 𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂ 𝑐 ⃗ = 3𝑖 ̂ − 4𝑗 ̂ + 5𝑘 ̂ [𝑎 ⃗,𝑏,𝑐 ⃗ ] = |■8(2&−1&1@1&2&−3@3&−4&5)| = 2[(2×5)−(−4×−3)] − (−1) [(1×5)−(3×−3) ] + 1[(1×−4)−(3×2) ] = 2 [10−12]+[5+9] + [−4−6] = –4 + 14 – 10 = 0 ∴ [𝒂 ⃗,𝒃,𝒄 ⃗ ] = 0 Therefore, 𝑎 ⃗,𝑏 and 𝑐 ⃗ are coplanar. Supplementary Exercise Q4 Show that (ii) the vectors 𝑎 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂, 𝑏 ⃗ = −2𝑖 ̂ + 3𝑗 ̂ − 4𝑘 ̂, and 𝑐 ⃗ = 𝑖 ̂ − 3𝑗 ̂ + 5𝑘 ̂ are coplanar Three vectors 𝑎 ⃗, 𝑏 ⃗, 𝑐 ⃗ are coplanar if [ 𝒂 ⃗, 𝒃 ⃗, 𝒄 ⃗ ] = 0 Given, 𝑎 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂ 𝑏 ⃗ = −2𝑖 ̂ + 3𝑗 ̂ − 4𝑘 ̂ 𝑐 ⃗ = 𝑖 ̂ − 3𝑗 ̂ + 5𝑘 ̂ [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) ] = 1 [15−12]+[2(−10−(−4)] + 3 [6−3] = 1(3) + 2 (−6) + 3 (3) = 3 − 12 + 9 = 12 − 12 = 0 ∴ [𝒂 ⃗,𝒃,𝒄 ⃗ ] = 0 Therefore, 𝑎 ⃗,𝑏 and 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