Example 25 - Chapter 10 Class 12 Vector Algebra (Important Question)

Last updated at Dec. 16, 2024 by

Example 25 - Find area of a parallelogram whose a = 3i + j + 4k

Example 25 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 25 Find the area of a parallelogram whose adjacent sides are given by the vectors (𝑎 ) ⃗ = 3𝑖 ̂ + 𝑗 ̂ + 4𝑘 ̂ and 𝑏 ⃗ = 𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ Given (𝒂 ) ⃗ = 3𝑖 ̂ + 1𝑗 ̂ + 4𝑘 ̂ 𝒃 ⃗ = 1𝑖 ̂ − 1𝑗 ̂ + 1k ̂ Area of parallelogram ABCD = |𝒂 ⃗ × 𝒃 ⃗ | Now, (𝒂 ) ⃗× 𝒃 ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@3&1&4@1&−1&1)| = 𝑖 ̂ (1 × 1 – (−1) × 4) − 𝑗 ̂ (3 × 1 – 1 × 4) + 𝑘 ̂ (3 × −1 − 1 × 1) = 𝑖 ̂(1 − (-4)) − j ̂ (3 − 4) + 𝑘 ̂ (−3 −1) = 𝑖 ̂(1 + 4) − j ̂ (−1) + 𝑘 ̂ (−4) = 5𝒊 ̂ + 𝒋 ̂ − 4𝒌 ̂ Magnitude of 𝑎 ⃗ × 𝑏 ⃗ = √(52+1^2+(−4)2) |𝒂 ⃗ × 𝒃 ⃗ | = √(25+1+16) = √𝟒𝟐 Area of parallelogram ABCD = |𝑎 ⃗ × 𝑏 ⃗ | = √42 Therefore, the required area is √𝟒𝟐 .

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo