This question is similar to Chapter 10 Class 12 Vector Algebra - Ex 10.3
Please check the question here

CBSE Class 12 Sample Paper for 2025 Boards
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Dec. 13, 2024 by Teachoo
This question is similar to Chapter 10 Class 12 Vector Algebra - Ex 10.3
Please check the question here
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