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 Oct. 1, 2019 by Teachoo

Question 10 (OR 2 nd question)

Find the angle between the vectors:

a = i + j – k and b = i – j + k

Find angle between vectors: a = i + j - k and b = i - j + k - Teachoo

Question 10 (Or 2nd) - CBSE Class 12 Sample Paper for 2019 Boards - Part 2

Question 10 (Or 2nd) - CBSE Class 12 Sample Paper for 2019 Boards - Part 3

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)

CBSE Class 12 Sample Paper for 2019 Boards

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Class 12

Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

CBSE Class 12 Sample Paper for 2021 Boards
CBSE Class 12 Sample Paper for 2020 Boards
CBSE Class 12 Sample Paper for 2019 Boards
CBSE Class 12 Sample Paper for 2018 Boards

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.