Chapter 10 Class 12 Vector Algebra
Ex 10.2, 9
Ex 10.2, 10 Important
Ex 10.2, 13 Important
Ex 10.2, 17 Important
Example 14 Important
Example 16 Important
Example 21 Important
Ex 10.3, 2
Ex 10.3, 3 Important
Ex 10.3, 10 Important
Ex 10.3, 13 Important
Ex 10.3, 16 Important
Example 23 Important
Example 24
Example 25 Important You are here
Ex 10.4, 2 Important
Ex 10.4, 5 Important
Ex 10.4, 9 Important
Ex 10.4, 10
Ex 10.4, 11 (MCQ) Important
Example 28 Important
Example 29 Important
Example 30 Important
Misc 6
Misc 12 Important
Misc 13
Misc 15 Important
Misc 19 (MCQ) Important
Chapter 10 Class 12 Vector Algebra
Last updated at April 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 .