#did i do right?
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ye this is good. can also notice certain vectors equal like vector AB = vector ED
@worldly basin has given 1 rep to @lyric ginkgo
That's incorrect.
At the very least, you can see that the vertical components of AC and BD have the same sign (in fact, they are the same). So, only the horizontal component of AC + BD is zero, but AC + BD isn't the zero vector.
And AC and BD are not parallel, obviously.
But you did write |AC + BD| = 0, which is not correct.
Why is AD + BC equal to the zero vector?
You can see from the picture that it isn't so.
No. Cross product of collinear vectors is always 0. The sum of collinear vectors u and v is only zero when they have the same magnitude, but opposite directions, so when u = -v.