if a → and b→ are prependicular unit vector and vector c→ is such that c→=a → +b→ ,then the value ofa→×b→.b→×c→+b→×c→.c→×a→+c→×a→.a→×b→
a→×b→.b→×c→+b→×c→.c→×a→+c→×a→.a→×b→
=a→·b→b→·c→-a→·c→b→·b→+b→·c→c→·a→-b→·a→c→·c→+c→·a→a→·b→-c→·b→a→·a→
=0-a→.c→+b→.c→c→.a→-0+0-c→.b→ since a→·b→=0 and a→=1 andb→=1
=b→.c→c→.a→-c→.a→-b→.c→+1-1
=b→.c→-1c→.a→-1-1 since b→·c→=a→·b→+b→·b→ =0+1=1 and similarly c→·a→=1
=1-11-1-1=-1