Check sibling questions

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Supplementary Exercise Q1 if 𝑎 ⃗ = 7𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂, 𝑏 ⃗ = 𝑖 ̂ − 𝑗 ̂ + 2𝑘 ̂ and 𝑐 ⃗ = 3𝑖 ̂ + 8𝑗 ̂ , then find 𝑎 ⃗ (𝑏 ⃗ × 𝑐 ⃗) and (𝑎 ⃗ × 𝑏 ⃗). 𝑐 ⃗ Also Find whether if 𝑎 ⃗.(𝑏 ⃗ × 𝑐 ⃗) and (𝑎 ⃗ × 𝑏 ⃗).𝑐 ⃗ are equal Given, 𝑎 ⃗ = 7𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂ , 𝑏 ⃗ = 𝑖 ̂ – 𝑗 ̂ + 2𝑘 ̂ , 𝑐 ⃗ = 3𝑖 ̂ + 8𝑗 ̂ = 3𝑖 ̂ + 8𝑗 ̂ + 0𝑘 ̂ 𝑎 ⃗.(𝑏 ⃗ × 𝑐 ⃗) = [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = |■8(7&−2&3@1&−1&2@3&8&0)| = 7[(−1×0)−(8×2) ] − (−2) [(1×0)−(3×2) ] + 3[(1×8)−(3×−1)] = 7 [0−16]+2(0−6)+3[8+3] = 7(–16) + 2(–6) + 3(11) = –112 – 12 + 33 = –91 Finding (𝑎 ⃗ × 𝑏 ⃗).𝑐 ⃗ = 𝑐 ⃗.(𝑎 ⃗ × 𝑏 ⃗) = [𝑐 ⃗" " 𝑎 ⃗" " 𝑏 ⃗ ] = |■8(3&8&0@7&−2&3@1&−1&2)| = 3[(−2×2)−(−1×3) ] − 8[(7×2)−(1×3) ] + 0[(7×−1)−(1×−2)] = 3[−4+3]−8(14−3)−0 = 3(–1) – 8(11) = –3 – 88 = –91 Hence , 𝒂 ⃗.(𝒃 ⃗ × 𝒄 ⃗) = (𝒂 ⃗ × 𝒃 ⃗).𝒄 ⃗

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.