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?

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.