1.

Let `hata,hatb` and `hatc` be unit vectors and `alpha, beta`, and `gamma` the angles between the vectors `hata,hatb,hatb,hatc` and `hatc, hata` respectively . If `hata + hatb+hatc` is also a unit vectors, then `cosalpha + cosbeta +cosgamma` is equal to -A. `-1`B. `3`C. `-3`D. `1`

Answer» Correct Answer - 1
`|hata|= |hatb|=|hatc|=1`
&`|hata +hatb+ hatc|=1" ".....(1)`
By (1)
`rArr |hata + hatb+ hatc|^(2)=1`
`|hata|^(2) +|hatb|^(2) + |hatc|^(2) + 2|hata||hatb| cos alpha + 2|hatb||hatc|cos beta +2 |hatc||hata| cos gamma=1`
`rArr 3+2 (cos alpha + cos beta + cos gamma)=-1`
`rArr (cos alpha + cos beta + cos gamma )=-1`


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