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Given the angle, how to calculate the modulus of a vector has a specific topic [senior one mathematics].
The square of the vector's modulus is equal to the square of the vector, which is the basic method to find the vector's modulus.

A, B bit unit vector, so |a|=|b|= 1.

|a+3b|？ =(a+3b)？ =a？ +6a？ b+9b？ =|a|？ +6|a|？ |b|？ cos60 +9|b|？ = 1+3+9= 13

So |a+3b|=√ 13

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