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 to

Options

A. 1
B. `1/8`
C. `-16/11`
D. `-11/16`

Answer

C

Explanation

`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`