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Given that a̅ = 3i̅ - 8j̅ + k̅ and b̅ = 4i̅ + 3j̅ - λk̅. If a̅ + b̅ = 7i̅ - 5j̅ - 3k̅, then the value of λ is:  

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AAI ATC Junior Executive 21 Feb 2023 Shift 1 Official Paper
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  1. 5
  2. 6
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 4 : 4
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Detailed Solution

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Given:

a̅ = 3i̅ - 8j̅ + k̅ and b̅ = 4i̅ + 3j̅ - λk̅.

If a̅ + b̅ = 7i̅ - 5j̅ - 3k̅,

Concept:

Use concept of sum of vectors.

And two vectors are equal when the coefficient of i , j and k are equal .

Calculation:

a̅ = 3i̅ - 8j̅ + k̅ and b̅ = 4i̅ + 3j̅ - λk̅. 

On comparing the coefficient on both the sides

the we get 

- 3 = 1 - λ

⇒ λ = 4

Hence the option (4) is correct.

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Last updated on Jun 19, 2025

-> The AAI ATC Exam 2025 will be conducted on July 14, 2025 for Junior Executive.. 

-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025. 

-> AAI JE ATC 2025 notification is released on April 4, 2025, along with the details of application dates, eligibility, and selection process.

-> A total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.

-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in the Airports Authority of India (AAI).

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-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).

-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.

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