Vector Equation found confusing...

SlowLearner007

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Sep 13, 2019
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Thanks all for answering my questions. A real challenge appears as the below question:

A triangular plate of uniform density and thickness has vertices at v1 = (0,1) v2 = (8,1), and v3 = (2,4)
and the mass of the plate is 3 g.

a) Find the (x,y) coordinates of the center of mass of the plate. This balance point of the plate coincides
with the center of mass of a system consisting of three 1-gram point masses located at the vertices of the plate.

b) Determine how to distribute an additional mass of 6 g at the three vertices of the plate to move the
balance point of the plate to (2,2).

For a), l would add the three vertices and divides the result by 3, so as (0,1) + (8,1) + (2,4) to give (10,6)
divided by 3 to get the answer (10/3, 2)

but for b), first let w1, w2 and w3 denote the masses added at the three vertices, so that w1 + w2 + w3 = 6

The vector equation appears in my mind as w1v1 + w2v2+ w3v3 = (2,2).... but w1 is the mass in gram , while
v1 is the x,y co-ordinates, can we write something as w1v1? Even the vector equation is acceptable,
w1, w2 ,and w3 have three entities, but the (x,y) co-ordinates just have two entities... so l have difference
in solving this question, please help.
 
You were given that v1= (0, 1), v2= (8, 2), and v3= (2, 4) so w1v1+ w2v2+ w3v3= (0, w1)+ (8w2, 2w2)+ (2w3, 4w3).
 
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