Supplementary Example 1 - Find a.(b x c), (a x b).c, Is - 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 Example 1 If 𝑎﷯ = 2 𝑖﷯ − 3 𝑗﷯ + 4 𝑘﷯ , 𝑏﷯ = 𝑖﷯ + 2 𝑗﷯ – 3 𝑘﷯ , 𝑐﷯ = 3 𝑖﷯ + 4 𝑗﷯ – 𝑘﷯, then find 𝑎﷯.( 𝑏﷯ × 𝑐﷯) & ( 𝑎﷯ × 𝑏﷯). 𝑐﷯ . Is 𝑎﷯.( 𝑏﷯ × 𝑐﷯) = ( 𝑎﷯ × 𝑏﷯). 𝑐﷯ ? Given, 𝑎﷯ = 2 𝑖﷯ − 3 𝑗﷯ + 4 𝑘﷯ , 𝑏﷯ = 𝑖﷯ + 2 𝑗﷯ – 3 𝑘﷯ , 𝑐﷯ = 3 𝑖﷯ + 4 𝑗﷯ – 𝑘﷯ 𝑎﷯.( 𝑏﷯ × 𝑐﷯) = 𝑎﷯ 𝑏﷯ 𝑐﷯﷯ = 2﷮−3﷮4﷮1﷮2﷮−3﷮3﷮4﷮−1﷯﷯ = 2 2×−1﷯−(4×−3) ﷯ − (−3) 1×−1﷯−(3×−3) ﷯ + 4 1×4﷯−(3×2)﷯ = 2 −2+12﷯+3 −1+9﷯+4 4−6﷯ = 2(10) + 3 (8) + 4(–2) = 20 + 24 – 8 = 36 Finding ( 𝑎﷯ × 𝑏﷯). 𝑐﷯ = 𝑐﷯.( 𝑎﷯ × 𝑏﷯) = 𝑐﷯ 𝑎﷯ 𝑏﷯﷯ = 3﷮4﷮−1﷮2﷮−3﷮4﷮1﷮2﷮−3﷯﷯ = 3 −3×−3﷯−(2×4) ﷯ − 4 2×−3﷯−(1×4) ﷯ + (–1) 2×2﷯−(1×−3)﷯ = 3 9−8﷯−4 −6−4﷯− 4+3﷯ = 3(1) – 4(–10) – 7 = 3 + 40 – 7 = 36 Hence , 𝑎﷯.( 𝑏﷯ × 𝑐﷯) = ( 𝑎﷯ × 𝑏﷯). 𝑐﷯

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