CBSE Class 12 Sample Paper for 2025 Boards
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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
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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
