Given that the magnitude of each of the two vectors

→

a

and

→

b

have same magnitude.
⇒ |

→

a

| = |

→

b

| ... (i)
the angle between

→

a

and

→

b

is 60°
⇒ θ = 60°
and

→

a

.

→

b

=

3

2

... (iii)
Since,

→

a

.

→

b

= |

→

a

| |

→

b

| cos θ
⇒ |

→

a

| |

→

a

| cos 60° =

9

2

From (i),(ii) and (iii)
⇒ |

→

a

|2 ×

1

2

=

9

2

⇒ |

→

a

|2 = 9
⇒ |

→

a

| = 3
⇒ |

→

a

| = |

→

b

| = 3 ... From (i)