JEE Advance - Mathematics (1984 - No. 19)

If $$\,{a^2} + {b^2} + {c^2} = 1$$, then ab + bc + ca lies in the interval

$$[{1 \over 2},2]\,\,$$

$$[ - 1,2]$$

$$\,[ - {1 \over 2},1]\,$$

$$\,[ - 1,{1 \over 2}]\,\,$$