Question
Download Solution PDFDetermine the vector equation of the plane passing through the intersection of the planes
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
As we know that, if a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0 represents two different planes, then equation of plane passing through the intersection of these planes is given by:
(a1x + b1y + c1z + d1) + λ × (a2x + b2y + c2z + d2) = 0.
Calculation:
Given:
Convert these planes in the cartesian form.
Put
So
⇒ x + y + z = 6 .........(1)
Similarly,
⇒ 2x + 3y + 4z = -5 .........(2)
So, the plane passing through the intersection of two given planes is:
⇒ (x + y + z – 6) + λ × (2x +3y + 4z + 5) = 0
∵ it is given that the plane passing through the intersection of two given planes also passes through the point (1, 1, 1)
⇒ The point (3, 2, 1) will satisfy equation (1)
⇒ (1 + 1 + 1 - 6) + λ × (2 + 3 + 4 + 5) = 0 ⇒ λ = 3/14.
So, by substituting the value of λ in equation (1), we get
⇒ (x + y + z – 6) + (3/14) × (2x +3y + 4z + 5) = 0
20x +23y + 26z = 69
Last updated on Jul 16, 2025
-> Predict Your Marks via AAI ATC Rank Predictor 2025 for free.
-> AAI ATC answer key 2025 has been released on July 16, 2025 at the official website.
-> Check the AAI ATC Exam Analysis 2025 for July 14, 2025 Exam.
-> AAI ATC admit card 2025 has been released.
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).
-> The Selection of the candidates is based on the Computer-Based Test, Voice Test and Test for consumption of Psychoactive Substances.
-> 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.
-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.