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.
Work Step by Step
(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.
