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

CBSE Class 12 Sample Paper for 2024 Boards
CBSE Class 12 Sample Paper for 2024 Boards
Last updated at Dec. 13, 2024 by Teachoo
This question is similar to Question-23-Choice-1 CBSE Class 12 Sample Paper for 2023 Boards
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)