Saved Bookmarks
| 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` |
|