Question 15 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at July 20, 2026 by Teachoo

The magnitude of projection of (2i − j + k ) on (i − 2j + 2k ) is _______

The magnitude of projection of (2i − j + k ) on (i − 2j + 2k ) is ___

Question 15 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2

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Transcript

Question 15 (OR 1st Question) The magnitude of projection of (2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂) on (𝑖 ̂ − 2𝑗 ̂ + 2𝑘 ̂) is _______ Projection of vector 𝒂 ⃗ on 𝒃 ⃗ = 𝟏/|𝒃 ⃗ | (𝒂 ⃗. 𝒃 ⃗) Let 𝑎 ⃗ = 2𝑖 ̂ – 𝑗 ̂ + 𝑘 ̂ 𝑏 ⃗ = 𝑖 ̂ – 2𝑗 ̂ + 2𝑘 ̂ (𝒂 ⃗ . 𝒃 ⃗) = (2 × 1) + (–1 × −2) + (1 × 2) = 2 + 2 + 2 = 6 Magnitude of 𝑏 ⃗ = √(12+(−2)2+22) |𝑏 ⃗ | = √(1+4+4) |𝑏 ⃗ | = √9 |𝑏 ⃗ | = 3 Projection of 𝑎 ⃗ on 𝑏 ⃗ = 1/|𝑏 ⃗ | (𝑎 ⃗. 𝑏 ⃗) = 1/3 × 6 = 2 ∴ Magnitude of projection is 2 units

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