The correct option is B 90∘,60∘
Suppose if possible b, c are collinear. Then b×c=0⇒a×(b×c)=0⇒12b=0⇒b=0
It is a contradiction to the fact that b is a unit vector. ∴b,c are non collinear.
a×(b×c)=12b⇒(a.c)b−(a.b)c=12b⇒(a.c−12)b−(a.b)c=0
⇒a.c−12=0,a.b=0 [Since b, c are not collinear]
a.b=0⇒(a,b)=90∘
a.c−12=0⇒a.c=12⇒|a||c|cos(a,c)=12⇒cos(a,c)=12⇒(a,c)=60∘