Check sibling questions

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

Example 22 - Chapter 10 Class 12 Vector Algebra - Part 2


Transcript

Example 22 Find |π‘Ž βƒ— Γ— 𝑏 βƒ—|, if π‘Ž βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ + 3π‘˜ Μ‚ and 𝑏 βƒ— = 3𝑖 Μ‚ + 5𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Given 𝒂 βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ + 3π‘˜ Μ‚ 𝒃 βƒ— = 3𝑖 Μ‚ + 5𝑗 Μ‚ βˆ’ 2π‘˜ Μ‚ Now, 𝒂 βƒ— Γ— 𝒃 βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@2&1&3@3&5&βˆ’2)| = 𝑖 Μ‚ (1 Γ— (-2) – 5 Γ— 3) βˆ’ 𝑗 Μ‚ (2 Γ— (-2) βˆ’ 3 Γ— 3) + π‘˜ Μ‚ (2 Γ— 5 βˆ’ 3 Γ— 1) = 𝑖 Μ‚ (βˆ’2 βˆ’15) βˆ’ 𝑗 Μ‚ (βˆ’4 βˆ’9) + π‘˜ Μ‚ (10 βˆ’ 3) = –17π’Š Μ‚ + 13𝒋 Μ‚ + 7π’Œ Μ‚ So, Magnitude of π‘Ž βƒ— Γ— 𝑏 βƒ— = √((βˆ’17)2+(13)2+(7)2) |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = √(289+169+49) = √507 Thus, |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = βˆšπŸ“πŸŽπŸ•

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