`[(a+b,b+c,c+a)]=[(a,b,c)]`, then

Options

A. `[(a,b,c)]=1`
B. a, b, c are coplanar
C. `[(a, b, c)]=-1`
D. a, b, c are mutually perpendicular

Answer

B

Explanation

Given, `[a+b" "b+c" "c+a]=[abc]`
`rArr" "(a+b)*{(b+c)xx(c+a)}=[abc]`
` implies (a+b).{bxxc+bxxa+cxxa}=[a" "b" "c][ :' cxxc =0]`
`rArr" "a*(bxxc)+bb*b(cxxa)=[abc]`
`rArr" "[abc]+[abc]=[abc]" "[bca]=[abc]]`
`rArr" "[abc]=0`
`rArr" a, b"` and c are cojplanar.