If a→,b→, and c→ are unit vectors such that a→+2b→+2c→=0→ , then |a→×c→| is equal to

2b→=−a→−2c→squaring both sides4b→2=a→2+4c→2+4a→.c→4=1+4+4a→.c→⇒a→.c→=−14a¯×c¯2=a¯2c¯2−a¯.c¯2=1-116=1516