If `veca,vecb` are vectors perpendicular to each other and `|veca|=2, |vecb|=3, vecc xx veca=vecb`, then the least value of `2|vecc-veca|` is

Options

A. 1
B. 2
C. 3
D. 4

Answer

C

Explanation

`vecc xx veca = vecb`
`rArr |vecc xx veca|=|vecb|`
`rArr |vecc||veca|sin(g)theta=3`
`rArr |vec|=3/(2sintheta)`
`|vecc-veca|^(2)=|vecc|^(2)+|veca|^(2)-2vecc.veca`
`=|vecc|^(2)+4-2|vecc|.|veca|costheta`
`=9/(4sin^(2)theta)+4-2.3/(sintheta).2.costheta`
`=4+9/4"cosec"^(2)theta-6cottheta`
`=9/4+(3/2cottheta-2)^(2)`
`rArr |vecc-veca|^(2)ge9/4 rArr |vecc-veca|ge3/2`
`rArr 2|vecc-veca|ge3`
`therefore "Min of " 2|vecc-veca|=3`