#### Answer

(a) Two vectors are parallel if they are scalar or multiples of each other. Also, the cross product is zero, that is:
$a \times b =0$ iff a and b are scalar multiples.
(b) Two vectors are perpendicular when the dot product is zero. that is,
$a \cdot b =0$ iff a and b are orthogonal or perpendicular.
(c) Two different planes are parallel iff their normal vectors are parallel to each other.