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If a(1) and a(2) are two values of a for...

If `a_(1) and a_(2)` are two values of a for which the unit vector `ahati+bhatj+(1)/(2) hatk` is linearly dependent with `hati+2hatj and hatj-2hatk`,then `(1)/(a_(1))+(1)/(a_(2))` is equal to

A

1

B

`1/8`

C

`-16/11`

D

`-11/16`

Text Solution

Verified by Experts

The correct Answer is:
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`
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