The point P(x, y) that minimize the sum of distances between the fixed points lying in a plane.
(a)
To Show:
That the condition is equivalent to .
(b)
To Show:
That the function is differentiable except at points A, B and C and the minimum of occurs either at P satisfying the equation , where e, f and g are the unit
(c)
To Prove:
That the equation , where e, f and g are the unit vectors in the direction of vectors holds if and only if P is the Fermat point, defined as the point P for which the angles between the segments and are all 120°.
(d)
To Show:
That the Fermat point does not exist if one of the angles in is greater than 120° and the point which exist in this case is different from Fermat point.
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