CBSE Class 12 Sample Paper for 2021 Boards

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

## Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors iΒ Μ - jΒ Μ + kΒ Μ and 4iΒ Μ + 5kΒ Μ

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Question 26 Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors π Μ β π Μ + π Μ and 4π Μ + 5π Μ Let ABCD be the parallelogram Where π β = π Μ β π Μ + π Μ And Diagonal π β = 4π Μ + 5π Μ Now, π β + π β = π β π β = π β β π β π β = (4π Μ + 5π Μ ) β (π Μ β π Μ + π Μ ) π β = 3π Μ + π Μ + 4π Μ Now, Area of parallelogram ABCD = |π β" Γ " π β | π β Γ π β = |β 8(π Μ&π Μ&π Μ@1&β1&1@3&1&4)| = π Μ (β1 Γ 4 β 1 Γ 1) β π Μ (1 Γ 4 β 3 Γ 1) + π Μ (1 Γ 1 β 3 Γ β1) = π Μ (β4 β 1) β π Μ (4 β 3) + π Μ (1 + 3) = β5π Μ β π Μ + 4π Μ Now, Area of Parallelogram ABCD = |(π¨π©) β Γ (π©πͺ) β | = β((β5)2+(β1)2+42) = β(25+1+16) = βππ square units