Question
Download Solution PDFDetermine the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 4x - 2y + 3z - 6 = 0
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The plane : 4x - 2y + 3z - 6 = 0
Concept:
For a plane having equation ax + by + cz = d(a, b, c) are direction ratios of the normal to the plane.
Equation of a line passing through (x1, y1, z1) and having direction ratios a, b, c in the cartesian form :
\(\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}= \frac{z-z_{1}}{c}\)
Calculation:
Direction ratios of normal to the plane are 4, -2, and 3.
Equation of a line passing through the origin (0, 0, 0) and having direction ratios 4, -2, 3 is:
\(\frac{x-0}{4}=\frac{y-0}{-2}= \frac{z-0}{3} = λ\)
⇒ x = 4λ , y = -2λ and z = 3λ
Satisfying equation of the plane with above coordinates :
⇒ 4(4λ) - 2(-2λ) + 3(3λ) - 6 = 0
⇒ λ = 6/29
∴ Foot of the perpendicular,
⇒ x = 24/29, y = -12/29 and z = 18/29
Last updated on May 26, 2025
-> AAI ATC exam date 2025 will be notified soon.
-> 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 4th April 2025, along with the details of application dates, eligibility, and selection process.
-> 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 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.