Adding Vectors!

[Calc12]

In the diagram attached: triangleABC is an equilateral and D,E,F are the midpoints of its sides.
Express each sum as a single vector.

Here is what I got, but I don't think it's right.

a) AF + DB = FD
b) DE + DB = EB
c) FA + EB = AD
d) DA + EC = AF
e) AF + DE = 0

Could someone please help me clarify?
I very much appreciate all help :shock:

 

[tkhunny]

Not real clear what is wanted.

Perhaps it will help to note that these three vectors are the same: AD, DB, and FE

 

[Deleted member 4993]

In the diagram attached: triangleABC is an equilateral and D,E,F are the midpoints of its sides.
Express each sum as a single vector.

Here is what I got, but I don't think it's right.

a) AF + DB = AF + AD = AE

b) DE + DB = AF + AD = AE

c) FA + EB = CF + CE = CD

d) DA + EC = ??

e) AF + DE = ??

Could someone please help me clarify?
I very much appreciate all help :shock:

 

[soroban]

Hello, Calc12!

In the diagram: triangle ABC is equilateral and D,E,F are the midpoints of its sides.

            C
            *
           / \
          /   \
       F *- - -* E
        / \   / \
       /   \ /   \
    A * - - * - - * B
            D

\(\displaystyle \text{Note that: }\;\begin{Bmatrix}\overrightarrow{AD} \;=\; \overrightarrow{DB} \;=\; \overrightarrow{FE} \\ \overrightarrow{AF} \;=\;\overrightarrow{FC} \;=\;\overrightarrow{DE} \\ \overrightarrow{BE} \;=\; \overrightarrow{EC} \;=\; \overrightarrow{DF} \end{Bmatrix}\)

Express each sum as a single vector.

\(\displaystyle (a)\;\overrightarrow{AF} +\overrightarrow{DB}\)

\(\displaystyle \overrightarrow{AF} + \overrightarrow{DB} \;=\;\overrightarrow{AF} + \overrightarrow{FE} \;=\;\overrightarrow{AE}\)

\(\displaystyle (b)\; \overrightarrow{DE} + \overrightarrow{DB}\)

\(\displaystyle \overrightarrow{DE} + \overrightarrow{DB} \;=\;\overrightarrow{AF} + \overrightarrow{FE} \;=\;\overrightarrow{AE}\)

\(\displaystyle (c)\; \overrightarrow{FA} + \overrightarrow{EB}\)

\(\displaystyle \overrightarrow{FA} + \overrightarrow{EB} \;=\;\overrightarrow{CF} + \overrightarrow{FD} \;=\;\overrightarrow{CD}\)

\(\displaystyle (d)\;\overrightarrow{DA} + \overrightarrow{EC}\)

\(\displaystyle \overrightarrow{DA} + \overrightarrow{EC} \;=\; \overrightarrow{BD} + \overrightarrow{DF} \;=\;\overrightarrow{BF}\)

\(\displaystyle (e)\; \overrightarrow{AF} + \overrightarrow{DE}\)

\(\displaystyle \overrightarrow{AF} + \overrightarrow{DE} \;=\;\overrightarrow{AF} + \overrightarrow{FC} \;=\;\overrightarrow{AC}\)

 

[Calc12]

thank you so much!