Find the vector equation of a line passing through the point A(1,-1,2) and perpendicular to the plane `vecr.(2hati-hatj+3hatk)=5`.

Explanation

The position vector of the given point is `vec a - ( hat I - hat j + 2 hat k)`
The givne plane is `vec r . Vec n `= q , where `vec n = (2 hat I - hat j + 3 hat k)` and q =5
Since the required line is perpendicular to the given plane so it must be parallel to its normal `vec n`
Thus we need a line whihc passes through a point having position vector ` vec a` and which is parallel to vector `vec n`
so its vector equation is
`vec r =vec a + lambda vec n , i.e vec r = (hat i- hat j + 2 hat k) + lambda (2 hat i - hat j + 3 hat k)`
for some scalar `lambda`