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Question 10 (Or 2nd) - CBSE Class 12 Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

Question 10 (OR 2 nd question)

Find the angle between the vectors:

  a = i + j – k and b = i – j + k

Transcript

Question 10 (OR 2nd question) Find the angle between the vectors: 𝑎 ⃗ = 𝑖 ̂ + 𝑗 ̂ – 𝑘 ̂ and 𝑏 ⃗ = 𝑖 ̂ – 𝑗 ̂ + 𝑘 ̂ Given 𝑎 ⃗ = 𝑖 ̂ + 𝑗 ̂ – 𝑘 ̂ and 𝑏 ⃗ = 𝑖 ̂ – 𝑗 ̂ + 𝑘 ̂ We know that 𝑎 ⃗ . 𝑏 ⃗ = |𝑎 ⃗ ||𝑏 ⃗ | cos θ where θ is the angle between 𝑎 ⃗ & 𝑏 ⃗ Now, 𝒂 ⃗. 𝒃 ⃗ = (𝑖 ̂ + 𝑗 ̂ – 𝑘 ̂). (𝑖 ̂ – 𝑗 ̂ + 𝑘 ̂) = (1𝑖 ̂ + 1𝑗 ̂ – 𝑘 ̂). (1𝑖 ̂ − 1𝑗 ̂ + 1𝑘 ̂) = 1 × 1 + 1 × (−1) + (-1) × 1 = 1 – 1 – 1 = –1 Magnitude of 𝑎 ⃗ = √(12+12+(−1)2) |𝑎 ⃗ |= √(1+1+1) = √3 Magnitude of 𝑏 ⃗ = √(12+(−1)2+12) |𝑏 ⃗ |= √(1+1+1) = √3 Now, 𝑎 ⃗ . 𝑏 ⃗ = |𝑎 ⃗ ||𝑏 ⃗ | cos θ –1 = √3 × √3 × cos θ –1 = 3 cos θ cos θ = (−1)/3 θ = 𝒄𝒐𝒔^(−𝟏) ((−𝟏)/𝟑) Thus, the angle between 𝑎 ⃗ and 𝑏 ⃗ is cos-1((−𝟏)/𝟑)
  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

    3. CBSE Class 12 Sample Paper for 2019 Boards

    CBSE Class 12 Sample Paper for 2018 Boards →
CBSE Class 12 Sample Paper for 2018 Boards →
Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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