Answer
(a) Parallel and point in the same direction.
(b) Not parallel.
(c) Parallel and point in the opposite direction.
(d) Not parallel.
Work Step by Step
(a) Since $ v=\langle 4,8,12\rangle = 2\langle 2,4,5\rangle $, then the vectors are parallel and have the same direction.
(b) Since there is no real number $ m $ such that $ v=\langle 4,8,12\rangle = m\langle-1,-2,3\rangle $, then the vectors are not parallel.
(c) Since $ v=\langle 4,8,12\rangle = -1.75\langle-7,-14,-21\rangle $, then the vectors are parallel. However, they point in opposite directions (negative sign).
(d) Since there is no real number $ m $ such that $ v=\langle 4,8,12\rangle = m\langle6,10,14\rangle $, then the vectors are not parallel.
