Q 2251880724.     If the vectors `vec(b) = ( tan alpha , -1,2 sqrt(sin alpha/2) )` and

`vec(c) = ( tan alpha , tan alpha , -3/sqrt(sin alpha/2) ) ` are orthogonal and a

vector `vec(a) = (1,3 , sin 2 alpha)` makes an obtuse angle with the

`z`-axis, then the value of `alpha` is

A

` alpha = (4n +1) pi - tan^(-1) 2`

B

` alpha = (4n +2) pi - tan^(-1) 2`

C

` alpha = (4n +1) pi + tan^(-1) 2`

D

` alpha = (4n +2) pi + tan^(-1) 2`

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