Mathematics

Problem

Three vectors

a(|a| \neq 0)

b

and

c

are such that a \times b = 3a \times c

, also

|a| = |b| = 1

and

|c| = \frac{1}{3}

. If the angle between

and

is

60^\circ

and

|b - 3c| = \lambda |a|

, then the value of

\lambda$ is