Q. 25.0( 1 Vote )

# Find the equation of the plane through the line of intersection of the planes x - 3y + z + 6 = 0 and x + 2y + 3z + 5 = 0, and passing through the origin.

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

x-3y + z + 6 + λ(x + 2y + 3z + 5)=0

(1 + λ)x + (-3 + 2λ)y + (1 + 3λ)z + 6 + 5λ=0 (2)

Now plane passes through (0,0,0) then it must satisfy the plane equation,

(1 + λ).0 + (-3 + 2λ).0 + (1 + 3λ).0 + 6 + 5λ=0

5λ=-6 Putting in equation (2)  -x-27y-13z=0

x + 27y + 13z=0

So, required equation of plane is x + 27y + 13z=0.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  The Embryonic Development62 mins  NCERT Exemplar Special | The Living World Part 225 mins  Nernst Equation - Learn the Concept33 mins  Understanding the Combination of cells54 mins  Revising the basics of Organic Chemistry35 mins  Types of solution on the basis of Raoult's Law44 mins  Nucleophilic Substitution Reaction | Getting the basics39 mins  Lets understand the ploidy levels of various structures of a flowering plant53 mins  Getting into the world of coliisionsFREE Class  Know About finding the Adjoint & Inverse Of Matrix46 mins
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 view all courses RELATED QUESTIONS :

Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers