I'm completely new to physics and currently doing summer homework for the AP Physics class I'm taking this coming year in high school. I just need some further explanation on some problems.

__Problem #1__
Can three or more vectors with unequal magnitudes be added together so their sum is zero? If so, show by means of tail-to-head arrangement of the vectors how this could occur.

I know that a vector is zero when its components are all zero. Knowing this does this mean if the components of

**A**,

**B**, and

**C** are all zero (all 6 components) then

**A**,

**B**, and

**C **is zero and their sum is zero? (0 + 0 + 0)

Am I on the right track? Could someone elaborate on the tail-to-head arrangement? I don't quite understand from the book.

__Problem #2__
A golfer, putting on a green, requires three strokes to “hole the ball.” During the first putt, the ball rolls 5.0 m due east. For the second putt, the ball travels 2.1 m at an angle of 20.0 north of east. The third putt is 0.50 m due north. What displacement (magnitude and direction relative to due east) would have been needed to “hole the ball” on the very first putt?

I've saw many replies on this one and they just confused me. Here my attempt as a picture:

So am I doing this right? Just solve for A? If so how?

I could find the other lengths using trig, but am I doing it right so far?