Consider the vectors a⃗ =4i⃗ +j⃗ −k⃗ ,b⃗ =i⃗ +j⃗ +5k⃗ ,c⃗ =i⃗ +4j⃗ −k⃗
d⃗ =−4i⃗ −j⃗ +k⃗ ,g⃗ =i⃗ −4j⃗ .
Which pairs (if any) of these vectors are

(a) Are perpendicular?

(Enter none or a pair or list of pairs, e. g., if a⃗ is perpendicular to b⃗ and c⃗ , enter (a, b),(a, c).)

(b) Are parallel?

(Enter none or a pair or list of pairs, e. g., if a⃗ is parallel to b⃗ and c⃗ , enter (a, b),(a, c).)

(c) Have an angles less than π/2 between them?

(Enter none or a pair or list of pairs, e. g., if a⃗ is at an angle less than pi/2 from b⃗ and c⃗ , enter (a, b),(a, c).)

(d) Have an angle of more than π/2 between them?