Caachy - Schurartz Inegliality

Given: $$ \begin{array}{l} u=(2,9,1) \\ v=(3,0,4) \\ \|u\|=\sqrt{2^{2}+3^{2}+1^{2}}=\sqrt{4+9+1}=\sqrt{14} \\ \|v\|=\sqrt{3^{2}+0^{2}+4^{2}}=\sqrt{9+0+16}=\sqrt{25}=5 \end{array} $$ Angle $\theta$ between two such vectors v $(3,0,4)$ and $4(2,3,1)$ is given by

$\cos \theta-\frac{u \sqrt{y}}{\|y\| \cdot\|u\|}$

$\cos \theta=\frac{(2 \times 3+3 \times 0+1 \times 4)}{5 \sqrt{14}}$

$=\frac{5+4}{5.70}$

$=\frac{2}{\sqrt{14}}$

$\theta=\cos ^{-1}\left(\frac{2}{\sqrt{14}}\right)$

$\theta=1.0069$