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 July 18, 2026 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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