If \( a^{2}+b^{2}+c^{2}=1 \), then \( a b+b c+c a \) lies in the interval
(a) \( \left[\frac{1}{...
If \( a^{2}+b^{2}+c^{2}=1 \), then \( a b+b c+c a \) lies in the interval
(a) \( \left[\frac{1}{2}, 2\right] \)
(b) \( [-1,2] \)
(c) \( \left[-\frac{1}{2}, 1\right] \)
(d) \( \left[-1, \frac{1}{2}\right] \)
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