Let `A` and `B` be two given points whose coordinate are respectively `(x_1 ,y_1, z_1)` and `(x_2, y_2, z_2)`
If `vec(a)` and `vec(b)` are p.v. of `A` and `B` relative to point `O`,then

`vec(a)= x_1 hat(i)+ y_1 hat(j)+ z_1 hat(k)`
`vec(b)= x_2 hat(i)+ y_2 hat(j)+ z_2 hat(k)`

Now `vec(AB) =vec(OB) -vec(OA) =vec(b)-vec(a) = (x_2 -x_1)hat(i)+ (y_2 -y_1)hat(j) +(z_2 -z_1)hat(k)`

Distance between the points `vec(A)` and `vec(B)` = magnitude of `vec(AB)` `= sqrt ( (x_2 -x_1)^2 + (y_2 -y_1)^2 + (z_2 -z_1)^2)`