Answer :

Equation of plane through the line of intersection of planes in Cartesian form is

(1)


For the standard equation of planes,



So, putting in equation (1), we have


2x + 3y–z + 1 + λ(x + y–2z + 3)=0


(2 + λ)x + (3 + λ)y + (-1-2λ)z + 1 + 3λ=0 (2)


Now as the plane 3x-y-2z-4=0 is perpendicular the given plane,


For θ=90°, cos90°=0


(3)


On comparing with standard equations in Cartesian form,



Putting values in equation (3), we have


(2 + λ).3 + (3 + λ).(-1) + (-1-2λ).(-2)=0


6 + 3λ-3-λ + 2 + 4λ=0


5 + 6λ=0



Putting in equation(2)




7x + 13y + 4z-9=0


7x + 13y + 4z=9


So, required equation of plane is 7x + 13y + 4z=9.


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