Question
Download Solution PDFFind a vector perpendicular to the plane that passes through the points P(1, 4, 6), Q(-2, 5, -1) and R(1, -1, 1).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
To find a vector perpendicular to the find two planes, first, find the vector in the plane and then take their cross product.
Solution:
Given, the plane is passing through the points P(1, 4, 6), Q(-2, 5, -1) and R(1, -1, 1).
Step (1) Find two vectors in the plane.
We will do this by finding the vector from (1, 4, 6) (-2, 5, -1) and (1, 4, 6) (1, -1, 1).
As all three points are in the plane, so will each of those vectors.
Step (2) Find a vector perpendicular to the plane.
If a vector is perpendicular to two vectors in a plane, it must be perpendicular to the plane itself. As the cross-product of two vectors produces a vector perpendicular to both, we will use the cross-product of
Hence, the vector perpendicular to the plane that passes through the points P(1, 4, 6), Q(-2, 5, -1), and R(1, -1, 1) is (-40, -15, 15).
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).
-> 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.