CBSE Class 12 Sample Paper for 2019 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 10 (OR 1 st question)

Find the area of the parallelogram whose diagonals are represented by the vectors a = 2iΒ  β 3jΒ  + 4k and b = 2i β j + 2k

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Question 10 (OR 1st question) Find the area of the parallelogram whose diagonals are represented by the vectors π β = 2π Μ β 3π Μ + 4π Μ and π β = 2π Μ β π Μ + 2π Μ Area of parallelogram with diagonals Area = 1/2 |(π_1 ) βΓ(π_2 ) β | Given Diagonals of a parallelogram as π β = 2π Μ β 3π Μ + 4π Μ and π β = 2π Μ β π Μ + 2π Μ Area of the parallelogram = 1/2 |π βΓπ β | Finding π β Γ π β π β Γ π β = |β 8(π Μ&π Μ&π Μ@2&β3&[email protected]&β1&2)| = π Μ ((β3) Γ 2 β (-1) Γ 4) β π Μ (2 Γ 2 β 2 Γ 4) + π Μ (2 Γ (-1) β 2 Γ (-3)) = π Μ (-6 + 4) β π Μ (4 β 8) + π Μ (β2 + 6) = π Μ (β2) - π Μ (β4) + π Μ (4) = β2π Μ + 4π Μ + 4π Μ So, Magnitude of π β Γ π β = β((β2)2+(4)2+(4)2) |π β" Γ " π β | = β(4+16+16) |π β" Γ " π β |= β36 |π β" Γ " π β |= 6 Thus, Area of the parallelogram = 1/2 |π βΓπ β | = 1/2 Γ 6 = 3 square units