    1. Chapter 10 Class 12 Vector Algebra (Term 2)
2. Serial order wise
3. Supplementary examples and questions from CBSE

Transcript

Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co –terminus edges are (i) 𝑎 ⃗ = 2𝑖 ̂ − 3𝑗 ̂ + 4𝑘 ̂, 𝑏 ⃗ = 3𝑖 ̂ − 𝑗 ̂ + 2𝑘 ̂, and 𝑐 ⃗ = 𝑖 ̂ + 2𝑗 ̂ − 𝑘 ̂, Given, 𝑎 ⃗ = 2𝑖 ̂ − 3𝑗 ̂ + 4𝑘 ̂ , 𝑏 ⃗ = 3𝑖 ̂ – 𝑗 ̂ + 2𝑘 ̂ , 𝑐 ⃗ = 𝑖 ̂ + 2𝑗 ̂ – 𝑘 ̂ Volume of parallelepiped = [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = |■8(2&−3&4@3&−1&2@1&2&−1)| = 2[(−1×−1)−(2×2) ] − (−3) [(3×−1)−(1×2) ] + 4[(3×2)−(1×−1)] = 2 [1−4]+3(−3−2)+4[6+1] = 2(–3) + 3 (–5) + 4(7) = –6 – 15 + 28 = 7 Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co –terminus edges are (ii) 𝑎 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂, 𝑏 ⃗ = 2𝑖 ̂ + 𝑗 ̂ − 𝑘 ̂, and 𝑐 ⃗ = 2𝑖 ̂ + 𝑗 ̂ − 𝑘 ̂, Given, 𝑎 ⃗ = 𝑖 ̂ − 2𝑗 ̂ + 3𝑘 ̂ , 𝑏 ⃗ = 2𝑖 ̂ + 𝑗 ̂ – 𝑘 ̂ , 𝑐 ⃗ = 2𝑖 ̂ + 𝑗 ̂ – 𝑘 ̂ Volume of parallelepiped = [𝒂 ⃗" " 𝒃 ⃗" " 𝒄 ⃗ ] = |■8(1&−2&3@2&1&−1@2&1&−1)| = 1[(1×−1)−(1×−1)] − (−2) [(2×−1)−(2×−1)] + 3[(2×1)−(2×1)] = 1 [−1+1]+2(−2+2)+3[2−2] = 1(0) + 2 (0) + 3(0) = 0

Supplementary examples and questions from CBSE 