What is a resultant vectors direction?

It depends. I do not know if you are adding vectors in 1D, 2D or even 3D.
In 1D: its direction is along the x axis if its positive, otherwise it is in the opposite direction
In 2D: its direction is along the x or y axis if its component is positive, otherwise it is in the opposite direction
In 3D: its direction is along the x, y or z axis if its component is positive, otherwise it is in the opposite direction

(a) 150 N

(b) 15.62 N

(c) 8.54 N

(d) 50 N

Explanation:

From the question above,

(a) F' = F₂-F₁

Where F' = Result force, F₁ = 50 N, F₂ = 200 N

Therefore,

F' = 200-50

F' = 150 N

(b) F' = √(F₁²+F₂²)

Where F₁ = 10 N, F₂ =12 N

F' = √(10²+12²)

F' = √(100+144)

F '= √(244)

F =15.62 N

(c)

F' = √[(F₁+F₂)²+F₃²]

Where F₁ = 6 N, F₂ = 2 N, F₃ = 3 N.

Therefore,

F' = √[(6+2)²+3²)

F' = √(8²+3²)

F' = √(64+9)

F' = √(73)

F' = 8.54 N.

(d)

F' = √[(F₁+F₂)²+(F₃+F₄)²]

Where F₁ = 20 N, F₂ = 10 N, F₃ = 20 N, F₄ = 20 N

F' = √[(20+10)²+(20+20)²]

F' = √[(30)²+(40)²]

F' = √[900+1600]

F' = √[2500]

F' = 50 N