a→,b→ and c→ are three coplanar unit vectors such that a→+b→+c→=0. If three vectors p→,q→ and r→  are parallel to a→,b→ and c→  respectively, and have integral but different magnitudes, then among the  following options |p→+q→+r→|  can take a value equal to

Let a→,b→ and c→ lie in the x−y plane.  Let a→=i^,b→=−12i^+32i^ and c→=−12i^−32j^Therefore, |p→+q→+r→|=|λa→+μb→+vc→|=λi^+μ−12i^+32j^+v−12i^−32j^=λ−μ2−v2i^+32(μ−v)j^=λ−μ2−v22+34(μ−v)2=λ2+μ2+v2−λμ−λv−μv=12(λ−μ)2+(μ−v)2+(v−λ)2≥121+1+4=3Hence |p→+q→+r→|  can take a value equal to 3 and 2