Example 22 - Find |a x b|, if a=2i+j+3k and b=3i+5j-2k - Vector product - Defination

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 22 Find | 𝑎﷯ × 𝑏﷯|, if 𝑎﷯ = 2 𝑖﷯ + 𝑗﷯ + 3 𝑘﷯ and 𝑏﷯ = 3 𝑖﷯ + 5 𝑗﷯ − 2 𝑘﷯ 𝑎﷯ = 2 𝑖﷯ + 𝑗﷯ + 3 𝑘﷯ 𝑏﷯ = 3 𝑖﷯ + 5 𝑗﷯ − 2 𝑘﷯ 𝑎﷯ × 𝑏﷯ = 𝑖﷯﷮ 𝑗﷯﷮ 𝑘﷯﷮2﷮1﷮3﷮3﷮5﷮−2﷯﷯ = 𝑖﷯ (1 × (-2) – 5 × 3) − 𝑗﷯ (2 × (-2) − 3 × 3) + 𝑘﷯ (2 × 5 − 3 × 1) = 𝑖﷯ (−2 −15) − 𝑗﷯ (−4 −9) + 𝑘﷯ (10 − 3) = 𝑖﷯ (−17) - 𝑗﷯ (−4 −9) + 𝑘﷯ (10 −3) = 𝑖﷯ (−17) − 𝑗﷯(−13) + 𝑘﷯(7) = –17 𝑖﷯ + 13 𝑗﷯ + 7 𝑘﷯ ∴ 𝒂﷯ × 𝒃﷯ = −17 𝒊﷯ + 13 𝒋﷯ + 7 𝒌﷯ So, Magnitude of 𝑎﷯ × 𝑏﷯ = ﷮ −17﷯2+ 13﷯2+ 7﷯2﷯ 𝑎﷯ × 𝑏﷯﷯ = ﷮289+169+49﷯ = ﷮507﷯ Thus, 𝑎﷯ × 𝑏﷯﷯ = ﷮𝟓𝟎𝟕﷯

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