If a,b,c are three vectors such that [abc]=5, then the value of [a×bb×cc×a] is

If a, b and c are three vectors such that [a b c]=1, then find the value of [a+b b+c c+a]+[ atimesb btimesc ctimesa ]

If a, b and c are three non-coplanar vectors, then find the value of (a*(btimesc))/(ctimes(a*b))+(b*(ctimesa))/(c*(atimesb)) .

If a, b and c are three non-coplanar vectors, then find the value of (a*(btimesc))/(ctimes(a*b))+(b*(ctimesa))/(c*(atimesb)) .

The three vectors a, b and c with magnitude 3, 4 and 5 respectively and a+b+c=0, then the value of a.b+b.c+c.a is

The three vectors a, b and c with magnitude 3, 4 and 5 respectively and a+b+c=0, then the value of a.b+b.c+c.a is

The three vectors a, b and c with magnitude 3, 4 and 5 respectively and a+b+c=0, then the value of a.b+b.c+c.a is

If a ,\ b ,\ c are real numbers such that |b+cc+a a+b c+a a+bb+c a+bb+cc+a|=0 , then show that either a+b+c=0 or, a=b=c .