Question

Find the equation of the plane which contains the line of intersection of the planes vector r.(i+2j+3k)-4=0,vector r.(2i+j-k)+5=0 and which is perpendicular to the plane vector r.(5i+3j-6k)+8=0.

Answer 1

The given two planes are

 vector r.(i+2j+3k)-4=0    .....(i)

and      vector r.(2i+j-k)+5=0 ........(ii)

The equation of a plane passing through line of intersection of the planes (i) and (ii) is given by

Since, the plane (iii) is perpendicular to the plane

vector r.(5i+3j-6k)+8=0    ......................(iv)

=> Normal vector of (iii) is perpendicular to normal vector of (iv)

Putting the value of λ in (iii) we get equation of required plane

[Note : Normals of two perpendicular planes are perpendicular to each other.