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Let veca and vecb be two vectors of equa...

Let `veca` and `vecb` be two vectors of equal magnitude 5 units. Let `vecp,vecq` be vectors such that `vecp=veca-vecb` and `vecq=veca+vecb`. If `|vecp xx vecq|=2{lambda-(veca.vecb)^(2)}^(1/2)`, then value of `lambda` is

A

25

B

125

C

625

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`vecp xx vecq = (veca-vecb) xx (veca+vecb)`
`=2(veca xx vecb)`
`rArr |vecp xx vecq|^(2)=4{|vecb|^(2)|veca|^(2)-(vecb.veca)^(2)}`
`rArr |vecp xx vecq|^(2) = 4{625-(vecb.veca)^(2)}`
`rArr |vecp xx vecq|=2{625-(veca.vecb)^(2)}^(1//2)`
`rArr lambda=625`
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Knowledge Check

  • Let veca and vecb be two orthogonal unit vectors and vecc is a vector such that vecc xx vecb = veca-vecc , then |vecc| is equal to

    A
    1
    B
    `sqrt2`
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    0
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    1
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    2
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    3

  • If veca, vecb are unit vectors such that |veca +vecb|=1 and |veca -vecb|=sqrt3 , " then " |3veca +2vecb|=

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    7
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    4
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    ` sqrt7`
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    `sqrt19`

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