∵|

a

|=1，|

b

|=2，向量

a

与

b

的夹角为

2π

3

，

∴

a

•

b

=1×2×cos

2π

3

=-1

∵

c

=

a

+2

b

∴|

c

|=|

a

+2

b

|=

a 2+4 a • b +4 b 2

=

1-4+16

=

13

故选A．