Example 14 - Chapter 10 Class 12 Vector Algebra

Last updated at April 16, 2024 by Teachoo

Example 14 - Find angle between vectors a=i+j-k and b=i-j+k

Example 14 - Chapter 10 Class 12 Vector Algebra - Part 2

Example 14 - Chapter 10 Class 12 Vector Algebra - Part 3

Next: Example 15 → Go Ad-free

Transcript

Example 14 Find angle ‘θ’ between the vectors 𝑎 ⃗ = 𝑖 ̂ + 𝑗 ̂ − 𝑘 ̂ and 𝑏 ⃗ = 𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂. Given 𝑎 ⃗ = 𝑖 ̂ + 𝑗 ̂ − 𝑘 ̂ 𝑏 ⃗ = 𝑖 ̂ – 𝑗 ̂ + 𝑘 ̂ We know that 𝒂 ⃗ . 𝒃 ⃗ = "|" 𝒂 ⃗"|" "|" 𝒃 ⃗"|" cos θ where θ is the angle between 𝑎 ⃗ and 𝑏 ⃗ Finding |𝒂 ⃗ |, |𝒃 ⃗ | and 𝒂 ⃗ . 𝒃 ⃗ Magnitude of 𝑎 ⃗ = √(12+1^2+(−1)2) |𝒂 ⃗ | = √(1+1+1) = √𝟑 Magnitude of 𝑏 ⃗ = √(12+(−1)2+12) |𝒃 ⃗ | = √(1+1+1) = √𝟑 Finding 𝒂 ⃗ . 𝒃 ⃗ 𝒂 ⃗ . 𝒃 ⃗ = (1𝑖 ̂ + 1𝑗 ̂ – 1𝑘 ̂). (1𝑖 ̂ − 1𝑗 ̂ + 1𝑘 ̂) = 1.1 + 1.(−1) + (−1)1 = 1 – 1 − 1 = −1 Now, 𝒂 ⃗ . 𝒃 ⃗ = "|" 𝒂 ⃗"|" "|" 𝒃 ⃗"|" cos θ Putting values −1 = √3 × √3 × cos θ −1 = 3 cos θ cos θ = (−1)/3 θ = cos−1 ((−𝟏)/𝟑) Therefore, the angle between 𝑎 ⃗ and 𝑏 ⃗ is cos-1((−1)/3)

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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 and Computer Science at Teachoo

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