Example 25 - Chapter 10 Class 12 Vector Algebra
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 .
Examples
Example 2 Important
Example 3 Important
Example 4
Example 5
Example 6 Important
Example 7
Example 8 Important
Example 9
Example 10
Example 11 (i) Important
Example 11 (ii) Important
Example 12 Important
Example 13
Example 14 Important
Example 15
Example 16 Important
Example 17
Example 18 Important
Example 19
Example 20
Example 21 Important
Example 22
Example 23 Important
Example 24
Example 25 Important You are here
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Example 30 Important
Example 26 (Supplementary NCERT)
Example 27 (Supplementary NCERT)
Example 28 (Supplementary NCERT) Important
Example 29 (Supplementary NCERT) Important
Example 30 (Supplementary NCERT) Important
Example 31 (Supplementary NCERT) Important
About the Author
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