Question

The angle between vector a and b is 60.what is the ratio of

a.b and a*b

Answer 1

if a and b are two vectors having angle α between them then
$|a.b| = ab \cos( \alpha ) \\ |a \times b| = ab \sin( \alpha ) \\ so \\ \frac{ |a.b| }{ |a \times b| } = cot \alpha$
here
$\alpha = 60 \\ so \\ \frac{ |a.b| }{ |a \times b| } = \cot(60) = \frac{1}{ \sqrt{3} }$
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