Examples

Chapter 10 Class 12 Vector Algebra
Serial order wise

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Example 25 Find the area of a parallelogram whose adjacent sides are given by the vectors (π ) β = 3π Μ + π Μ + 4π Μ and π β = π Μ β π Μ + π Μ Given (π ) β = 3π Μ + 1π Μ + 4π Μ π β = 1π Μ β 1π Μ + 1k Μ Area of parallelogram ABCD = |π β Γ π β | Now, (π ) βΓ π β = |β 8(π Μ&π Μ&π Μ@3&1&[email protected]&β1&1)| = π Μ (1 Γ 1 β (β1) Γ 4) β π Μ (3 Γ 1 β 1 Γ 4) + π Μ (3 Γ β1 β 1 Γ 1) = π Μ(1 β (-4)) β j Μ (3 β 4) + π Μ (β3 β1) = π Μ(1 + 4) β j Μ (β1) + π Μ (β4) = 5π Μ + π Μ β 4π Μ Magnitude of π β Γ π β = β(52+1^2+(β4)2) |π β Γ π β | = β(25+1+16) = βππ Area of parallelogram ABCD = |π β Γ π β | = β42 Therefore, the required area is βππ .

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.