Question 24 (A) - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at February 13, 2025 by Teachoo

This question is similar to Chapter 10 Class 12 Vector Algebra - Ex 10.3

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https://www.teachoo.com/3412/746/Ex-10.3--10---If-a--b--c-are-such--a---b-is-perpendicular-to-c/category/Ex-10.3/

[Class 12 SQP] Question 24 (A) - If vectors 𝑎⃗ = 2ı̂ + 2ȷ̂ + 3k ̂, 𝑏 - CBSE Class 12 Sample Paper for 2025 Boards part 2 - Question 24 (A) - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

Question 24 (A) If vectors 𝑎 ⃗=2𝑖 ˆ+2𝚥 ˆ+3𝑘 ˆ,𝑏 ⃗=−𝚤 ˆ+2𝚥 ˆ+𝑘 ˆ and 𝑐 ⃗=3𝑖 ˆ+𝚥 ˆ are such that 𝑏 ⃗+𝜆𝑐 ⃗ is perpendicular to 𝑎 ⃗, then find the value of 𝜆.Given 𝑎 ⃗ = 2𝑖 ̂ + 2𝑗 ̂ + 3𝑘 ̂ 𝑏 ⃗ = −𝑖 ̂ + 2𝑗 ̂ + 𝑘 ̂ 𝑐 ⃗ = 3𝑖 ̂ + 𝑗 ̂ Now, (𝒃 ⃗ + 𝜆𝒄 ⃗) = (−𝑖 ̂ + 2𝑗 ̂ + 𝑘 ̂) + 𝜆 (3𝑖 ̂ + 𝑗 ̂) = −𝑖 ̂ + 2𝑗 ̂ + 𝑘 ̂ + 3𝜆𝑖 ̂ + 𝜆𝑗 ̂ = (3𝜆 − 1) 𝒊 ̂ + (2 + 𝜆) 𝒋 ̂ + 𝒌 ̂ Since (𝒃 ⃗ + 𝜆𝒄 ⃗) is perpendicular to 𝒂 ⃗ And, since Dot product of perpendicular vectors is 0 Therefore, (𝒃 ⃗ + 𝜆𝒄 ⃗). 𝒂 ⃗ = 0 ["(3𝜆 − 1) " 𝑖 ̂" + (2 + 𝜆) " 𝑗 ̂" + " 𝑘 ̂ ] . (2𝑖 ̂ + 2𝑗 ̂ + 3𝑘 ̂) = 0 (3𝜆 − 1) × 2 + (2 + 𝜆) × 2 + 1 × 3 = 0 6𝜆 − 2 + 4 + 2𝜆 + 3 = 0 8𝜆 + 5 = 0 8𝜆 = −5 𝜆 = (−𝟓)/𝟖

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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 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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