If `a_(1)` and `a_(2)` are two values of a for which the unit vector `aveci + bvecj +1/2veck` is linearly dependent with `veci+2vecj` and `vecj-2veck`, then `1/a_(1)+1/a_(2)` is equal toA. 1B. `1/8`C. `-16/11`D. `-11/16`

If `a_(1)` and `a_(2)` are two values of a for which the unit vector `

1.	If `a_(1)` and `a_(2)` are two values of a for which the unit vector `aveci + bvecj +1/2veck` is linearly dependent with `veci+2vecj` and `vecj-2veck`, then `1/a_(1)+1/a_(2)` is equal toA. 1B. `1/8`C. `-16/11`D. `-11/16`
Answer» Correct Answer - C `ahati+bhatj+1/2hatk=l(hati+2hatj)+m(hatj-2hatk)` `rArr a=l, b=2l+m` and `m=-1/4` `ahati+bhatj+1/2hatk` is unit vector `therefore a^(2)+b^(2)=3/4` `rArr 5a^(2)-a-11/16=0` `a_(1)` and `a_(2)` are roots of above equation `rArr 1/a_(1)+1/a_(2)=(a_(1)+a_(2))/(a_(1)a_(2))=-16/11`