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

Options

A. 25
B. 125
C. 625
D. none of these

Answer

C

Explanation

`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`