Find the vector equation of plane passing through thein tersection of planes `vec r. (hat i + 3hat j-hat k) ) = 5 and vec r* (2hat i -hat j +hat k) = 3` and point `(2, 1, -2)`.

Explanation

The given planes are,

`vecr*(hati+hatj+hatk)=6`

And, `vecr*(2hati+3hatj+4hatk)=-5`

Then, the cartesian form of the above two equations are,

`x+y+z-6=0`

And, `2x+3y+4z+5=0`

Now, the cartesian equation of the plane passing through the intersection of the given two planes is,

`[x+y+z-6]+lambda[2x+3y+4z+5]=0`
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