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Let a,bgt0 and alpha=(hati)/(a)+(4hatj)/...

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

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 alpha, beta be such that pi lt alpha lt beta lt 3pi, if sin alpha + sin beta =- (21)/(65) and cos alpha + cos beta =(27)/(65), then the value of cos ""(alpha - beta)/(2) is-

    A
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  • If alpha, beta (alpha ne beta) satisfy the equation a cos theta + b sin theta=c then the value of tan ""(alpha + beta)/(2) is-

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    D
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  • Let tanalpha=a/(a+1) and tan beta=1/(2a+1) then alpha+beta is

    A
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    B
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    C
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