Q. 84.3( 8 Votes )

Find the equation

Answer :

We know that solution of a plane passing through (x1,y1,z1) is given as -


a(x – x1) + b(y – y1) + c(z – z1) = 0


The required plane passes through (1, – 1, 2), so the equation of plane is


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


Plane (i) is also passing through (2, – 2, 2), so(2, – 2, 2) must satisfy the equation of plane, so we have


a(2 – 1) + b(– 2 + 1) + c(2 – 2) = 0


a – b = 0 …… (ii)


Plane 6x – 2y + 2z = 9 is perpendicular to the required plane


We know that planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0 are at right angles if,


a1a2 + b1b2 + c1c2 = 0 …… (a)


Using (a) we have,


a(6) + b(– 2) + c(2) = 0


6a – 2b + 2c = 0 …… (iii)


Solving (ii) and (iii) we get,





a = – 2λ, b = – 2λ, c = 4λ


Putting values of a,b,c in equation (i) we get,


(– 2λ)(x – 1) + (– 2λ)(y + 1) + (4λ)(z – 2) = 0


– 2λx + 2λ – 2λy – 2λ + 4λz – 8λ = 0


– 2λx – 2λy + 4λz – 8λ = 0


Dividing by – 2λ we get,


x + y – 2z + 4 = 0


So, the required plane is x + y – 2z + 4 = 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