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we start at AI started at the corner opposite A, at the other end of the diagonal of the parallelogram, in order to end up at A
"parallel to the diagonal".The translational position of a vector in a force diagram is irrelevant (unless you're dealing with torques)
length of ADI take it that D is now our label for the corner of the parallelogram opposite A,
The [square of the] length of the diagonal AD is b²+c²-2bc.cos(A)Are we using different D?
an angle like B+C does not occurAn angle with magnitude B+C occurs in the parallelogram of which AB abd AC are adjacent sides.
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and extending it once in the AB direction and twice in the AC direction,
We can start at the corner opposite to A of the parallelogram of which AB abd AC are adjacent sides (A+AB+AC)
From there, go to A+AB+AC+AB to A+AB+AC+AB+2BC to A+AB+AC+AB+2BC+3CA
and you will find yourself back at A, the other end of the diagonal.
The length of the diagonal is b²+c²+2bc.cos(A)