Epinephrine's noobalicious questions

[epinephrine]

So I decided to make a thread for all of my unit 2 GMA questions.

1. ORST is a parallelogram. U is the midpoint of RS and V is the midpoint of ST. Relative to
the origin O, r, s, t, u and v are the position vectors of R, S, T, U and V respectively.
(a) Express s in terms of r and t.
(b) Express v in terms of s and t.
(c) Hence or otherwise show that 4 (u + v) = 3 (r + s + t)

Did parts (a) and (b) but got stuck on (c), any help is greatly appreciated.

[Mao]

v = 0.5r + t
u = r + 0.5 t
s = r + t

4 (u + v) = 6 r + 6 t = 3 r + 3 t + (3r + 3t) = 3r + 3t + 3s = 3(r + s + t)

[epinephrine]

Thank you.

[epinephrine]

Could someone please explain how the principle of argument of z works please?

And possibly how to derive the angles within the domain -pi<theta<pi and how does that domain even work?

Any help would be greatly appreciated.

[Greatness]

When you convert from cartesian to polar form you get an angle i.e. the argument. If a question asks for the 'Argument' it means that theta/the argument is restricted to . If the argument is outside of this restriction you can add or subtract from it, as this gives you the same angle.

[epinephrine]

Thanks heaps Swarley !