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Homework Statement
Under what restrictions on ##c, d, e##, will the combinations ##c\vec u + d\vec v + e\vec w## fill in the dashed
triangle?
Homework Equations
The Attempt at a Solution
Clearly, ##\vec w + a (\vec v - \vec w) + b(\vec u - \vec v)## will be in the triangle when ##0 \leq b \leq a \leq 1## ;
##\vec w + a (\vec v - \vec w) + b(\vec u - \vec v) = b\vec u + (a-b) \vec v + (1-a)\vec w ##
So, we have ##c=b, a-b=d, e=1-a##
The restrictions are ,therefore ,
##c+d+e=1##
##0\leq c \leq 1,~ 0\leq d \leq 1,~ 0 \leq e\leq 1##
But according to the book, the restrictions are, ##c+d+e=1;~ 0\leq c ,~ 0\leq d ,~ 0 \leq e;##
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