1.

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

Answer»

`[(a,b,c)]=1`
a, b, c are coplanar
`[(a, b, c)]=-1`
a, b, c are mutually perpendicular

Solution :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.


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