We know that Electric Dipole Moment is given by P=q(2a). Here, 2a is a distance and hence is scalar. Also, q is scalar. The product of two scalars is also a scalar. Then how can P be a vector ?

see dipole moment is a vector quantity,it's magnitude is given by P=q*2a.,direction is from -ve to +ve. do not mix magnitude wid direction

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Dipole moment is a vector as it has a direction . It is directed from -q to +q. 
So dipole moment is defined as p = 2a x q  p cap where p cap is a vector directed from -q to +q. Hope that helps.
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