Question 16 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by Teachoo

The value of λ for which two vectors 2i ˆ-j ˆ+2k ˆ and 3i ˆ+λj ˆ+k ˆ are perpendicular is

(a) 2 (b) 4 (c) 6 (d) 8

This question is similar to Question-23-Choice-1 CBSE Class 12 Sample Paper for 2023 Boards

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Transcript

Two vectors 𝑝 ⃗ and 𝑞 ⃗ are perpendicular if their scalar product is zero, i.e. 𝒑 ⃗ . 𝒒 ⃗ = 0 Since 2𝑖 ˆ−𝑗 ˆ+2𝑘 ˆ and 3𝑖 ˆ+𝜆𝑗 ˆ+𝑘 ˆ are perpendicular to each other. Thus, (2𝒊 ̂ − 𝒋 ̂ + 2𝒌 ̂) . (3𝒊 ̂ + ("𝜆" 𝒋) ̂ + 𝒌 ̂) = 0 (2 × 3) + (-1 × 𝜆) + (2 × 1) = 0 6 − 𝜆 + 2 = 0 8 = 𝜆 𝜆 = 8 So, the correct answer is (d)

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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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