Supplementary examples and questions from CBSE

Chapter 10 Class 12 Vector Algebra
Serial order wise

Transcript

Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co βterminus edges are (i) π β = 2π Μ β 3π Μ + 4π Μ, π β = 3π Μ β π Μ + 2π Μ, and π β = π Μ + 2π Μ β π Μ, Given, π β = 2π Μ β 3π Μ + 4π Μ , π β = 3π Μ β π Μ + 2π Μ , π β = π Μ + 2π Μ β π Μ Volume of parallelepiped = [π β" " π β" " π β ] = |β 8(2&β3&4@3&β1&2@1&2&β1)| = 2[(β1Γβ1)β(2Γ2) ] β (β3) [(3Γβ1)β(1Γ2) ] + 4[(3Γ2)β(1Γβ1)] = 2 [1β4]+3(β3β2)+4[6+1] = 2(β3) + 3 (β5) + 4(7) = β6 β 15 + 28 = 7 Supplementary Exercise Q3 Find the volumes of the following parallelepipeds whose three co βterminus edges are (ii) π β = π Μ β 2π Μ + 3π Μ, π β = 2π Μ + π Μ β π Μ, and π β = 2π Μ + π Μ β π Μ, Given, π β = π Μ β 2π Μ + 3π Μ , π β = 2π Μ + π Μ β π Μ , π β = 2π Μ + π Μ β π Μ Volume of parallelepiped = [π β" " π β" " π β ] = |β 8(1&β2&3@2&1&β1@2&1&β1)| = 1[(1Γβ1)β(1Γβ1)] β (β2) [(2Γβ1)β(2Γβ1)] + 3[(2Γ1)β(2Γ1)] = 1 [β1+1]+2(β2+2)+3[2β2] = 1(0) + 2 (0) + 3(0) = 0