Question

If a vector + b vector + c vector = 0 then find value of a cector × b vector + b vector × c vector + c vector × a vector

Answer 1

Answer: f  a→≠0→ ,  b→≠0→  and  c→≠0→  then

a→+b→+c→=0→  implies that the vectors  a→,b→,c→  are not linearly independent as there is a non-zero combination  x→=(1,1,1)  which produces  0→ .

Since the vectors are not linearly independent one of the vector lies is the subspace spanned by the other two. In this case all the vectors can be on a line or a plane with the sum  a→+b→+c→  being  0→