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Let a,b gt 0 and vecalpha=(veci/a+(4hatj...

Let `a,b gt 0` and `vecalpha=(veci/a+(4hatj)/b+bhatk)` and `vecbeta = bhati+ahatj+1/bhatk`, then the maximum value of `10/(5 + vecalpha.vecbeta)` is

A

1

B

2

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
`vecalpha.vecbeta = b/a+(4a)/(b)+1ge5`
So, `(10/(5 + vecalpha.vecbeta))_("max")=1`.
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Knowledge Check

  • Let a,bgt0 and alpha=(hati)/(a)+(4hatj)/(b)+bhatk and beta=bhati+ahattj+(1)/(b)hatk , then the maximum value of (10)/(5+alpha*beta) is

    A
    1
    B
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    C
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    D
    8

  • Let vecalpha=(1)/(a)hati+(4)/(b)hatj+bhatk and vecbeta=bhati+ahatj+(1)/(b)hatk(Aaa, b gt 0) , then the maximum value of (12)/(6+vecalpha.vecbeta)) is

    A
    `(12)/(11)`
    B
    2
    C
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    D
    `(10)/(9)`

  • If a,bgt0 then the maximum value of (a^(3)b)/((a+b)^(4)), is

    A
    `(81)/(512)`
    B
    `(27)/(256)`
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