If →a,→b →c are unit vectors such that →a+→b+→c=→0,then the value of →a.→b+→b.→c+→c.→a is
(a) 1 (b) 3
(c) −32 (d) None of these
(c)We have,→a+→b+→c=0 and →a2=1,→b2=1,→c2=1∵ (→a+→b+→c)(→a+→b+→c)=0⇒→a2+→a.→b+→a.→c+→b.→a+→b2+→b.→c+→c.→a+→c.→b+→c2=0⇒ →a2+→b2+→c2+2(→a.→b+→b.→c+→c.→a)=0 [∵→a.→b=→b.→a,→b.→c=→c.→b and →c.→a=→a.→c]⇒ 1+1+1+2(→a.→b+→b.→c+→c.→a)=0⇒ →a.→b+→b.→c+→c.→a=−32