Ex 10.5, 1 (Supplementary NCERT)

Transcript

Ex 10.5, 1 (Supplementary NCERT)Find [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] if 𝑎 ⃗ = 𝑖 ̂ – 2𝑗 ̂ + 3𝑘 ̂ , 𝑏 ⃗ = 2𝑖 ̂ – 3𝑗 ̂ + 𝑘 ̂ , 𝑐 ⃗ = 3𝑖 ̂ + 𝑗 ̂ – 2𝑘 ̂Given, 𝑎 ⃗ = 𝑖 ̂ – 2𝑗 ̂ + 3𝑘 ̂ , 𝑏 ⃗ = 2𝑖 ̂ – 3𝑗 ̂ + 𝑘 ̂ , 𝑐 ⃗ = 3𝑖 ̂ + 𝑗 ̂ – 2𝑘 ̂ 𝑎 ⃗.(𝑏 ⃗ × 𝑐 ⃗) = [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = |■8(1&−2&3@2&−3&1@3&1&−2)| = 1[(−3×−2)−(1×1) ] − (–2)[(2×−2)−(3×1) ] + 3[(2×1)−(3×−3)] = 1 [6−1]+2(−4−3)+3[2+9] = 1(5) + 2(–7) + 3(11) = 5 – 14 + 33 = 38 – 14 = 24 ∴ [𝑎 ⃗" " 𝑏 ⃗" " 𝑐 ⃗ ] = 24