Angle θ between two vectors is given by, [tex] \theta =cos^{-1}( \frac{u \cdot v}{|u||v|} )[/tex]; where [tex]u \cdot v=2(3)+(-4)(-8)=6+32=38[/tex]; [tex]|u|= \sqrt{ 2^{2} + (-4)^{2} } = \sqrt{4+16} = \sqrt{20} [/tex] and [tex]|v|=\sqrt{ 3^{2} + (-8)^{2} } = \sqrt{9+64} = \sqrt{73}[/tex].
Therefore, [tex]\theta =cos^{-1}( \frac{38}{ \sqrt{20} \times \sqrt{73} } )=cos^{-1}0.9945=6.0^o[/tex]
