CBSE Class 12 Sample Paper for 2024 Boards

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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 July 23, 2026 by

The value of Ī» for which two vectors 2iĀ Ė†-jĀ Ė†+2kĀ Ė† and 3iĀ Ė†+Ī»jĀ Ė†+kĀ Ė† are perpendicular is

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

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

The value of Ī» for which two vectors 2i - j + 2k & 3i + Ī»j + k are - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 16 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

Two vectors š‘ āƒ— and š‘ž āƒ— are perpendicular if their scalar product is zero, i.e. š’‘ āƒ— . š’’ āƒ— = 0 Since 2š‘– Ė†āˆ’š‘— Ė†+2š‘˜ Ė† and 3š‘– Ė†+šœ†š‘— Ė†+š‘˜ Ė† are perpendicular to each other. Thus, (2š’Š Ģ‚ āˆ’ š’‹ Ģ‚ + 2š’Œ Ģ‚) . (3š’Š Ģ‚ + ("šœ†" š’‹) Ģ‚ + š’Œ Ģ‚) = 0 (2 Ɨ 3) + (-1 Ɨ šœ†) + (2 Ɨ 1) = 0 6 āˆ’ šœ† + 2 = 0 8 = šœ† šœ† = 8 So, the correct answer is (d)

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