Question 26 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors i ̂ - j ̂ + k ̂ and 4i ̂ + 5k ̂

Find area of the parallelogram whose one side and a diagonal are

Question 26 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

Transcript

Question 26 Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors 𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ and 4𝑖 ̂ + 5𝑘 ̂ Let ABCD be the parallelogram Where 𝒂 ⃗ = 𝒊 ̂ − 𝒋 ̂ + 𝒌 ̂ And Diagonal 𝑑 ⃗ = 4𝑖 ̂ + 5𝑘 ̂ Now, 𝒂 ⃗ + 𝒃 ⃗ = 𝒅 ⃗ 𝑏 ⃗ = 𝑑 ⃗ − 𝑎 ⃗ 𝑏 ⃗ = (4𝑖 ̂ + 5𝑘 ̂ ) − (𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ ) 𝒃 ⃗ = 3𝒊 ̂ + 𝒋 ̂ + 4𝒌 ̂ Now, Area of parallelogram ABCD = |𝑎 ⃗" × " 𝑏 ⃗ | 𝒂 ⃗ × 𝒃 ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@1&−1&1@3&1&4)| = 𝑖 ̂ (−1 × 4 − 1 × 1) − 𝑗 ̂ (1 × 4 − 3 × 1) + 𝑘 ̂ (1 × 1 − 3 × −1) = 𝑖 ̂ (−4 − 1) − 𝑗 ̂ (4 − 3) + 𝑘 ̂ (1 + 3) = −5𝒊 ̂ − 𝒋 ̂ + 4𝒌 ̂ Now, Area of Parallelogram ABCD = |(𝑨𝑩) ⃗ × (𝑩𝑪) ⃗ | = √((−5)2+(−1)2+42) = √(25+1+16) = √𝟒𝟐 square units

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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