Find `V_(ab)` in an electric field
`E = (2 hat(i) +3 hat(j)+4 hat(k))(N)/(C)`
where, `r_(a)=(hat(i)-2 hat(j)+hat(k))m`
and `r_(b)=(2 hat(i)+hat(j)-2 hat(k))m`.

Explanation

Here, the given field is uniform (constant). So,
`d V = - vec E . d vec r`
or `V_(ab) = V_a - V_b = - int _b^a vec E . d vec r`
=`-int_((2","1","-2))^((1","-2","1)) (2 hat i + 3 hat j + 4 hat k). (d x hat i + d y hat j + d z hat k)`
=`- int_((2","1","-2))^((1","-2","1))(2 d x + 3 d y + 4 d z)`
=`-[2 x + 3 y + 4 z]_((2","1","-2))^((1","-2","1)) = -1 V`.