# Problem set: vectors

#### matrix_204

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.
-------A_____________________E
--------\70°-------------70°/
---------\-----------------/
----------\---------------/
----------B\_____________/D
and
-------------B_________D
-------------|\-------/|
---------W?--|-\-----/-| W?[down]
-------[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.

-----------------o
----------------/|
---o----------/--|
---|\-------/----|
---|--\---/------|
---|----|--------|
---3----4--------5

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

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