Question
Download Solution PDFThe equation of the plane which contain the points (0, 6, 0) and (-2, -3, 4) and which is parallel to the ray with direction ratios (2, 3, -2) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The plane which contain the points (0, 6, 0) and (-2, -3, 4)
and parallel to the ray with direction ratios (2, 3, -2)
Concept:
The equation of a plane which passed through a point \(\rm (x_1,y_1,z_1)\) with normal vector is \(\rm (a,b,c)\)
\(\rm a(x-x_1)+b(y-y_1)+c(z-z_1)=0\)
Calculation:
The equation of the plane passes through (0,6,0) is
\(\rm ax+b(y-6)+cz=0......(1)\)
This plane passes through (-2,-3,4) then
\(\rm a(-2)+b(-3-6)+c(4)=0\)
\(\rm \implies-2a-9b+4c=0.......(2)\)
Plain (1) is parallel to the ray with direction ratios (2, 3, -2)
\(\rm 2a+3b-2c=0......(3)\)
Now, solving the equations (1), (2) and (3)
\(\rm \begin{vmatrix} x & y-6& z\\ -2 & -9 & 4\\ 2 & 3 & -2 \end{vmatrix} =0\)
\(\rm \implies x(18-12)-(y-6)(4-8)+z(-6+18)=0\)
\(\rm \implies 6x+4y-24+12z=0\)
\(\rm \implies 3x+2y+6z-12=0\)
Hence the option (2) is correct.
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.