Let `oversetto a=3hati+2hatj+xhatk` and `oversettob=hati-hatj+hatK`
Some real x. Then `|oversettoaxxoversettob|=r` is possible if:

Options

A. ` 3 sqrt ((3 )/(2)) lt r lt 5sqrt ((3)/(2)) `
B. ` 0 lt r le sqrt ((3)/(2)) `
C. ` r ge 5 sqrt (( 3 )/(2)) `
D. `sqrt (( 3 ) /(2) lt r le 3 sqrt ((3 ) /(2))`

Explanation

` veca xx vecb = |{:( hati ,, hatj,, hatk ), ( 3,,2,, x ) , ( 1,, -1,, 1):}|, | veca xx vecb | = sqrt ( 2 x ^ 2 - 2x + 38 ) = r `
` rArr r ge sqrt((75)/(2)) rArr r ge 5 sqrt ((3 )/(2)) `