Supplementary Exercise Q1 - Find a.(b x c) and (a x b).c. - Supplementary examples and questions from CBSE

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Supplementary Exercise Q1 if 𝑎﷯ = 7 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯, 𝑏﷯ = 𝑖﷯ − 𝑗﷯ + 2 𝑘﷯ and 𝑐﷯ = 3 𝑖﷯ + 8 𝑗﷯ , then find 𝑎﷯ ( 𝑏﷯ × 𝑐﷯) and ( 𝑎﷯ × 𝑏﷯). 𝑐﷯ Also Find whether if 𝑎﷯.( 𝑏﷯ × 𝑐﷯) and ( 𝑎﷯ × 𝑏﷯). 𝑐﷯ are equal Given, 𝑎﷯ = 7 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯ , 𝑏﷯ = 𝑖﷯ – 𝑗﷯ + 2 𝑘﷯ , 𝑐﷯ = 3 𝑖﷯ + 8 𝑗﷯ = 3 𝑖﷯ + 8 𝑗﷯ + 0 𝑘﷯ 𝑎﷯.( 𝑏﷯ × 𝑐﷯) = 𝑎﷯ 𝑏﷯ 𝑐﷯﷯ = 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﷯﷯ = 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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