Write the vector equation of the plane, passing through the point `(a ,\ b ,\ c)` and parallel to the plane ` -> rdot( hat i+ hat j+ hat k)=2.`

Explanation

Given plane is , `vecr.(hati+hatj+hatk) = 2 "….."(1)`
Equation of a plane parallel to plane(1) is
`vecr.(hati+hatj+hatk) = d"……"(2)`
`rArr (xhati+yhatj+ zhatk) . (hati+hatj+hatk) =d`
It passes through the point `(a,b,c)`.
`:. (ahati+bhatj+chatk).(hati+hatj+hatk) = d rArr a+b+c=d`
Put `vecr=xhati+yhatj+zhatk` and `d = a+b+c` in equation (2)
`(xhati+yhatj+zhatk).(hati+hatj+hatk) = a+b+c`
`rArr x+y+z=a+b+c`
which is the equation of required plane.