Ex 10.4, 1 - Chapter 10 Class 12 Vector Algebra

Transcript

Ex 10.4, 1 Find |𝑎 ⃗×𝑏 ⃗ |, if 𝑎 ⃗ = 𝑖 ̂ − 7𝑗 ̂ + 7𝑘 ̂ and 𝑏 ⃗ = 3𝑖 ̂ − 2𝑗 ̂ + 2𝑘 ̂𝑎 ⃗ = 𝑖 ̂ − 7𝑗 ̂ + 7𝑘 ̂ = 1𝑖 ̂ − 7𝑗 ̂ + 7𝑘 ̂ 𝑏 ⃗ = 3𝑖 ̂ − 2𝑗 ̂ + 2k ̂ 𝑎 ⃗ × 𝑏 ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@█(1@3)&█(−7@−2)&█(7@2))| = 𝑖 ̂ |■8(−7&7@−2&2)| −𝑗 ̂ |■8(1&7@3&2)| + k ̂ |■8(1&−7@3&−2)| = 𝑖 ̂ ("−7 × 2 – (−2 × 7)" ) − 𝑗 ̂((1×2 ) − (3×7 )) + 𝑘 ̂((1×2 ) − (3 × −7)) = 𝑖 ̂ (−14−(−14)) − 𝑗 ̂(2−21 ) + 𝑘 ̂((−2−(−21)) = 𝑖 ̂ (0) − 𝑗 ̂ (−19) + 𝑘 ̂(19) = 0𝑖 ̂ + 19𝑗 ̂ + 19𝑘 ̂ ∴ 𝒂 ⃗ × 𝒃 ⃗ = 0𝒊 ̂ + 19𝒋 ̂ + 19𝒌 ̂ Magnitude of 𝑎 ⃗ × 𝑏 ⃗ = √(02+192+192) |𝒂 ⃗" ×" 𝒃 ⃗ | = √(0+361+361) = √722 = √(19×19×2 ) = 19√𝟐 Therefore, the magnitude of 𝑎 ⃗" ×" 𝑏 ⃗ is 19√𝟐.