CBSE Class 12 Sample Paper for 2024 Boards

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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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

Last updated at August 4, 2026 by

If a =4i ˆ+6j ˆ and b =3j ˆ+4k ˆ, then the vector form of the component of a  along b  is

(a) 18/5 (3i ˆ+4k ˆ )                            (b) 18/25 (3j ˆ+4k ˆ )

(c) 18/5 (3i ˆ+4k ˆ )                            (d) 18/25(4i ˆ+6j ˆ)

[MCQ] If a = 4i + 6j, b = 3j + 4k, then vector component of a along b - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 12 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12
part 3 - Question 12 - 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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Now, Vector component of š‘Ž āƒ— along š‘ āƒ— = Projection Ɨ Unit vector of š’ƒ āƒ— = šŸ/("|" š’ƒ āƒ—"|" ) (š‘Ž āƒ—. š‘ āƒ—) Ɨ š‘ āƒ—/(|š‘ āƒ—|) = ((š‘Ž āƒ—". " š‘ āƒ—)/怖\ |š‘ āƒ—|怗^2 ) š‘ āƒ— ) Now, š’‚ āƒ— = 4š‘– Ė†+6š‘— Ė† = šŸ’š’Š Ė†+šŸ”š’‹ Ė† + 0 š’Œ Ė† š’ƒ āƒ— = 3š‘— Ė†+4š‘˜ Ė† = 0š’Š Ė† + šŸ‘š’‹ Ė†+šŸ’š’Œ Ė† Finding š’‚ āƒ—. š’ƒ āƒ— (š’‚ āƒ—. š’ƒ āƒ—) = (4 Ɨ 0) + (6 Ɨ 3) + (0 Ɨ 4) = 0 + 18 + 0 = 18 Magnitude of š‘ āƒ— = āˆš(02+32+42) |š’ƒ āƒ— | = āˆš(0+9+16) = āˆš25 = 5 Now, Vector component of š‘Ž āƒ— along š‘ āƒ— = ((š‘Ž āƒ—". " š‘ āƒ—)/怖\ |š‘ āƒ—|怗^šŸ ) š‘ āƒ— = 18/怖\ 5怗^šŸ (3š‘— Ė†+4š‘˜ Ė†) = šŸšŸ–/šŸšŸ“ (šŸ‘š’‹ Ė†+šŸ’š’Œ Ė† ) So, the correct answer is (b)

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