Problem set: vectors

could someone please help me with some of these probelms. i needed really soon, thanx alot

1. Let a=(1,1) and b=(4,2). Verify that
|a-(projection of a onto b)| <= |a-kb|, for all k any R.

2. ABCDE is a flexible string with AB=BC=CD=DE and AE horizontal. Masses are attached each exerting forces as shown. Find W.
---------W?--|-\-----/-| W?[down]
------------------C and <c=120°
-----------------800 N[down}

the length of BD on both diagrams is same except i couldn't make it much clear, u should get the idea by the angles between them.

3. Three masses of 3 kg, 4kg, and 5kg are attached to strings as shown in the diagram. the weights are released and the system reaches equilibrium. Describe final position of the weights.


consider the o's to be the two pulleys or something, and the lines are the strings.
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