Answer :

Given: Plane passes through A(2, 2, 1) and B(9, 3, 6). Plane is perpendicular to 2x + 6y + 6z = 1


To find: Equation of the plane


Formula Used: Equation of a plane is


a(x – x1) + b(y – y1) + c(z – z1) = 0


where a:b:c is the direction ratios of the normal to the plane.


(x1, y1, z1) is a point on the plane.


Explanation:


Let the equation of plane be a(x – x1) + b(y – y1) + c(z – z1) = 0


Since (2, 2, 1) is a point in the plane,


a(x – 2) + b(y – 2) + c(z – 1) = 0 … (1)


Since B(9, 3, 6) is another point on the plane,


a(9 – 2) + b(3 – 2) + c(6 – 1) = 0


7a + b + 5c = 0 … (1)


Since this plane is perpendicular to the plane 2x + 6y + 6z = 1, the direction ratios of the normal to the plane will also be perpendicular.


So, 2a + 6b + 6c = 0 a + 3b + 3c = 0 … (2)


Solving (1) and (2),





a : b : c = 3 : 4 : -5


Substituting in (1),


3x – 6 + 4y – 8 – 5z + 5 = 0


3x + 4y – 5z – 9 = 0


Therefore the equation of the plane is 3x + 4y – 5z – 9 = 0

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the equationMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the distanceMathematics - Board Papers

Find the coordinaMathematics - Board Papers

Find the CartesiaMathematics - Board Papers

Find the coordinaMathematics - Board Papers