Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Sept. 14, 2018 by Teachoo

Find the Projection (vector) of 2i − j + k on i − 2j + k

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here https://www.teachoo.com/cbse/sample-papers/

Find Projection (vector) of 2i - j + k on i - 2j + k - Teachoo

Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2

Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Part 3

Transcript

Question 11 Find the Projection (vector) of 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ on 𝑖 ̂ − 2𝑗 ̂ + 𝑘 ̂ Let a = 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ and b = 𝑖 ̂ − 2𝑗 ̂ + 𝑘 ̂ We need to find Projection (vector) of 𝑎 ⃗ on 𝑏 ⃗ Theory We know that Projection of 𝑎 ⃗ on 𝑏 ⃗ = 1/("|" 𝑏 ⃗"|" ) (𝑎 ⃗. 𝑏 ⃗) But here, we are asked projection (vector) So, we multiply projection by 𝑏 ⃗/|𝑏 ⃗ | Projection (vector) of 𝑎 ⃗ on 𝑏 ⃗ = 1/|𝑏 ⃗ | (𝑎 ⃗. 𝑏 ⃗) × 𝑏 ⃗/|𝑏 ⃗ | = ((𝑎 ⃗ . 𝑏 ⃗ ))/|𝑏 ⃗ |^2 × 𝑏 ⃗ (𝒂 ⃗. 𝒃 ⃗) = (2 × 1) + (–1 × –2) + (1 × 1) = 2 + 2 + 1 = 5 Magnitude of 𝑏 ⃗ = √(12+(−2)2+12) |𝑏 ⃗ | = √(1+4+1) = √6 Projection (vector) of 𝒂 ⃗ on 𝒃 ⃗ = ((𝑎 ⃗ . 𝑏 ⃗ ))/|𝑏 ⃗ |^2 × 𝑏 ⃗ = 5/(√6)^2 × ( 𝑖 ̂ − 2𝑗 ̂ + 𝑘 ̂) = 𝟓/𝟔 ( 𝒊 ̂ − 2𝒋 ̂ + 𝒌 ̂)

CBSE Class 12 Sample Paper for 2018 Boards

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Chapter 1 Class 8 Rational Numbers →

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.