If $|AB|=a$ and $|CD|=c$ what is the sum of $\overrightarrow{BA}+\overrightarrow{DC}=?$
Lets have a trapezoid ABCD with bases AB and CD.
$|AB|=a$
$|CD|=c$
$a\geq c$
Calculate the length of vectors:
- $\overrightarrow{BA}+\overrightarrow{DC}=$ strictly theoretical this would be $= -\overrightarrow{AB}+(-\overrightarrow{CD})= -\overrightarrow{a}+(-\overrightarrow{c})=-\overrightarrow{a}-\overrightarrow{c}$
In the solutions there is written: $\overrightarrow{a}-\overrightarrow{c}$
Where the heck did I made a mistake?
The same happened when calculating $\overrightarrow{AB}-\overrightarrow{DC}=\overrightarrow{a}+\overrightarrow{c} \implies $the official solution is $\overrightarrow{a}-\overrightarrow{c}$
and $\overrightarrow{BC}-\overrightarrow{AD}=-\overrightarrow{a}-\overrightarrow{c} \implies $the official solution is $\overrightarrow{a}-\overrightarrow{c}$
I also drew a picture and drew all the vectors. But the official solutions aren't making any sense. Are they wrong? Or did I made a colossal mistake somewhere?