As the title says, I've been trying to solve this for about 3 hours and im absolutely stumped. It's 3:50am. Any method i've tried has come out wrong and I'm in desperate need for these answers so i can go to bed. Question instructions say "solve the below system". PLEASE HELP!!!

Hi! I've been stuck on this problem for a while now, so I decided to text it out on another app and finally ask for help. I managed to find the magnitude on my own, but I honestly can't figure out how to find the direction, or what I'm doing wrong. I've watched several videos on it and have tried to go step by step, but any answer I try is marked wrong, (I do use an online school program.) I also didn't wanna cheat, (at least without knowing exactly how to do it and being able to replicate it) so as I've already said above, I didn't know what to do other than ask for help somewhere else. A step-by-step breakdown of what your meant to do would be great!

Also I know the post title says grade 12, while from my knowledge trig is done in 11th usually. It just kind of happened that way, so I'm not sure why I'm doing it a year late. Better late than never, though!

can someone help explain to me how to do 1b. I don’t understand what it’s asking. What i’ve done was with help and i still don’t understand how it works.

Prompt: "Use propositional logic to prove the arguments valid; you may use any of the equivalence or inference rules."

I have this sequence but I'm not confident in #4-7

1. A v B (hyp)
2. A → C (hyp)
3. B → C (hyp)
4. (A v B)’’ (1, Double negation)
5. (A’ ^ B’)’ (4, de morgan)
6. (A’)’ (5, simplification)
7. C (2, 6 modus ponens)

---
*UPDATE*

I currently have this sequence. I was struggling, then I realised the implication rule has an error (It says 'P -> Q is equivalent to P' v Q) so I wanted to get others input on if my work is correct.

1. A v B [hyp]
2. A → C [hyp]
3. B → C [hyp]
4. A’ v C [2, implication]
5. B’ v C [3, implication]
6. (A’ v C) ^ (B’ v C) [4, 5 conjunction]
7. (C v A’) ^ (C v B’) [6, commutative]
8. C v (A’ ^ B’) [7, distributive]
9. (A’ ^ B’) v C [8, commutative]
10. (A v B)’’ [1, double negation]
11. (A’ ^ B’)’ [10, de morgan]
12. C [9, 11 disjunctive syllogism]

My additional explanation for getting #12. disjunctive syllogism

P v Q, P’ < = > Q

(A’ ^ B’) v C, (A’ ^ B’)’ < = > C