If `hata,hatb and hatc` are three unit vectors such that `hata + hatb + hatc` is also a unit vector and `theta_(1),theta_(2) and theta_(3)` are angles between the vectors `hata,hatb,hatb,hatc and hatc,hata,` respectively m then among `theta _(1),theta_(2)and theta_(3)`

Options

A. all are acute angles
B. all are right angles
C. at least one is obtuse angle
D. none of these

Answer

c

Explanation

`|veca+vecb+vecc|^(2)=1`
`Rightarrow |veca|^(2)+|vecb|^(2) +|vecc|^(2)+2|veca||vecb|costheta_(1)`
` + 2|vecb||vecc|costheta_(2)+2|vecc||veca|costheta_(3)=1`
`Rightarrow costheta_(1)+costheta_(2)+costheta_(3)=-1`
Hence, one of `theta_(1),theta_(2) and theta_(3)` should be an obtuse angle.