If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are unit vectors, then \( |\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\overrightarrow{\mathfrak{c}}-\vec{a}|^2 \) does not exceed:
\[ |a - b|^2 + |b - c|^2 + |c - a|^2 \] \[ = 2 (a^2 + b^2 + c^2) - 2 (a \cdot b + b \cdot c + c \cdot a) \] \[ = 2 \times 3 - 2 (a \cdot b + b \cdot c + c \cdot a) \] \[ = 6 - \{(a + b + c)^2 - a^2 - b^2 - c^2\} \] \[ = 9 - |a + b + c|^2 \leq 9 \]
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