1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
  3. Examples
Check sibling questions

Example 15 - Chapter 10 Class 12 Vector Algebra

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Example 15 If 𝑎 ⃗ = 5𝑖 ̂ − 𝑗 ̂ − 3𝑘 ̂ and 𝑏 ⃗ = 𝑖 ̂ + 3𝑗 ̂ − 5𝑘 ̂ , then show that the vectors 𝑎 ⃗ + 𝑏 ⃗ and 𝑎 ⃗ − 𝑏 ⃗ are perpendicular. Two vectors 𝑝 ⃗ and 𝑞 ⃗ are perpendicular if their scalar product is zero, i.e. 𝒑 ⃗ . 𝒒 ⃗ = 0 Finding (𝒂 ⃗ + 𝒃 ⃗) and (𝒂 ⃗ − 𝒃 ⃗) (𝒂 ⃗ + 𝒃 ⃗) = (5 + 1) 𝑖 ̂ + (−1 + 3) 𝑗 ̂ + (−3 + (−5)) 𝑘 ̂ = 6𝒊 ̂ + 2𝒋 ̂ − 8𝒌 ̂ (𝒂 ⃗ − 𝒃 ⃗) = (5 − 1) 𝑖 ̂ + (−1 − 3) 𝑗 ̂ + (−3 − (−5)) 𝑘 ̂ = 4𝒊 ̂ − 4𝒋 ̂ + 2𝒌 ̂ We have to show that (𝑎 ⃗ + 𝑏 ⃗) and (𝑎 ⃗ − 𝑏 ⃗) are perpendicular to each other. So, we need to show (𝒂 ⃗ + 𝒃 ⃗) . (𝒂 ⃗ − 𝒃 ⃗) = 0 Solving LHS (𝒂 ⃗ + 𝒃 ⃗) . (𝒂 ⃗ − 𝒃 ⃗) = (6𝑖 ̂ + 2𝑗 ̂ − 8𝑘 ̂) . (4𝑖 ̂ − 4𝑗 ̂ + 2𝑘 ̂) = (6 × 4) + (2 × −4) + (−8 × 2) = 24 − 8 −16 = 0 Since (𝑎 ⃗ + 𝑏 ⃗) . (𝑎 ⃗ − 𝑏 ⃗) = 0 Hence, (𝑎 ⃗ + 𝑏 ⃗) is perpendicular to (𝑎 ⃗ − 𝑏 ⃗)
  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise

    3. Examples

    Miscellaneous →
Miscellaneous →
Chapter 10 Class 12 Vector Algebra
Serial order wise

About the Author

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 and Computer Science at Teachoo