Vectors Question

[viral niche]

Can someone please solve this and either send me the step solution or explain me how you did it

[viral niche]

This is the answer

Sorry for the quality

[hallow night]

We note that $$\vec{AF}+\vec{AC}=\vec{AB}+\vec{AE}=\vec{AD}$$
As such
$$\vec{AF}+\vec{AC}+\vec{AB}+\vec{AE}+\vec{AD} = 3\vec{AD}$$
$||\vec{AD}||=2$ since $ABCDEF$ is a regular hexagon with unit (1) side lengths, which can be divided into 6 congruent equilateral triangles. So
$3\vec{AD}$ has magnitude 6 and direction $\vec{AD}$, note that the angle between $\vec{AB}$ and $\vec{AD}$ is $60^{\circ}$.

[dusty field]

Crystopher

[viral niche]

Then the answer AB is wrong then right?

[hallow night]

not really, it says $60^{\circ}$ to $\vec{AB}$

[dusty field]

Crystopher

[hallow night]

which is in other words the direction of $\vec{AD}$

[dusty field]

Crystopher

[hallow night]

So the answer is correct, although it could be expressed in a simpler way.

[viral niche]

How do you know if the angle is 60 degrees?

Since only the corners of the hexagon are 60 degrees

[hallow night]

the triangle marked is equilateral

all of its angles are $60^{\circ}$

[dusty field]

Crystopher

[hallow night]

So this angle is $60^{\circ}$

[dusty field]

Crystopher

[hallow night]

this image describes it in better quality

[viral niche]

OOOHH my bad I thought that the corners are 60 but their all 120 sorry