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If veca,vecb are vectors perpendicular t...

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

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`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`
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