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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 `aveci + bvecj +1/2veck` is linearly dependent with `veci+2vecj` and `vecj-2veck`, 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)/(2)hatk=l(hati+2hatj)+m(hatj-2hatk)`
`implies a=l,b=2l+m and m=(-1)/(4)`
`ahati+bhatj+(1)/(2) hatk` is unit vector
`therefore a^(2)+b^(2)=(3)/(4)implies5a^(2)-a-(11)/(16)=0`
`a_(1) and a_(2)` are roots of above equation
`implies(1)/(a_(1))+(1)/(a_(2))=(a_(1)+a_(2))/(a_(1)a_(2))=-(16)/(11)`.
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