Can you solve this problem? I tried everything...

[lowkeyking]

 

[Dr.Peterson]

Please show what you tried:

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I might start by defining vectors u = AB and v = AD, and expressing various vectors in terms of those. The goal is to show that vector AE is parallel to vector AC.

 

[pka]

View attachment 22617

First note that \(\overrightarrow {AC}=\overrightarrow {AD}+\overrightarrow {DC}\)
Being a parallelogram we have \(\overrightarrow {DC}=\overrightarrow {AB}\).
Moreover, \(\overrightarrow {DC}=\overrightarrow {AB}=2\overrightarrow {AI}\).
Now you need to show that \(\overrightarrow {AC} \) is a multiple of \(\overrightarrow {AE} \)
If you post your work, we can help.