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 planes are parallel if their normal vectors are parallel, that is, their normal vectors are multiples of 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 planes are parallel if their normal vectors are parallel, that is, their normal vectors are multiples of each other.
