Find `V_(ab)` in a uniform electric field `vecE=(2hati+3hatj+4hatk)(N)/(C)`
where `vec(r_(a))=(hati-2hatj+hatk)mandvec(r_(b))=(2hati+hatj-2hatk)m`
where `vec(r_(a))=(hati-2hatj+hatk)mandvec(r_(b))=(2hati+hatj-2hatk)m`

Explanation

Here, the given field is uniform (cosntant). So using,
`dV=-vecE.dvecr or V_(ab)=V_(a)-V_(b)=-underset(b)overset(a)intvecE.dvecr`
`=underset("(2,1,-2)")overset("(1,-2,1)")int(2hati+3hatj+4hatk).(dxhati+dyhatj+dzhatk)=-underset("(2,1,-2)")overset(("1,-2,1"))int(2dx+3dy+4dz)`
`=-[2x+3y+4z]_("(2,1,-2)")^(("1,-2,1"))=-1` volt