find the value of x for which the angle between vectors A=2x^2 i+4xj+k and B=7i-2j+ xk

(where i,j k are unit vectors ) is obtuse.

book solution. let theta is the angle between A and B .now cos(theta)={A.B}/{|A|B|}<0

where | | means magnitude.then after that A.B<0(now my doubt is that why they not consider the bound -1<cos(theta)<0 by which one must get -|A||B|< A.B<0 according to them the answer is x lies in (0,1/2).what about the left bound -|A||B|.if we consider this bound question becomes very typical

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