Question 8 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

The scalar projection of the vector 3i ̂-j ̂-2k ̂ 𝑜𝑛 𝑡ℎ𝑒 𝑣𝑒𝑐𝑡𝑜𝑟 i ̂+2j ̂-3k ̂ is

(a) 7/√14

(b) 7/14

(c) 6/13

(d) 7/2

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Transcript

Question 8 The scalar projection of the vector 3𝑖 ̂−𝑗 ̂−2𝑘 ̂ 𝑜𝑛 𝑡ℎ𝑒 𝑣𝑒𝑐𝑡𝑜𝑟 𝑖 ̂+2𝑗 ̂−3𝑘 ̂ is (a) 7/√14 (b) 7/14 (c) 6/13 (d) 7/2 Let a = 3𝑖 ̂ − 𝑗 ̂ − 2𝑘 ̂ and b = 𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂ We need to find Projection of 𝑎 ⃗ on 𝑏 ⃗ We know that Projection of 𝑎 ⃗ on 𝑏 ⃗ = 𝟏/("|" 𝒃 ⃗"|" ) (𝒂 ⃗. 𝒃 ⃗) Now, (𝒂 ⃗. 𝒃 ⃗) = (3𝑖 ̂ − 𝑗 ̂ − 2𝑘 ̂ ) . (𝑖 ̂ + 2𝑗 ̂ − 3𝑘 ̂) = (3 × 1) + (–1 × 2) + (−2 × −3) = 7 Magnitude of 𝑏 ⃗ = √(12+22+(−3) 2) |𝒃 ⃗ | = √(1+4+9) = √𝟏𝟒 Thus, Projection of 𝒂 ⃗ on 𝒃 ⃗ = 1/("|" 𝑏 ⃗"|" ) (𝑎 ⃗. 𝑏 ⃗) = 𝟕/√𝟏𝟒 So, the correct answer is (a)

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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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