$c\left(\alpha ,\beta \right)c\left(\beta ,\alpha \right)$

$c\left(\alpha ,\beta \right)$

$c\left(\beta ,\alpha \right)$

${\Vert \beta \Vert }^2/{\Vert \alpha \Vert }^2$

$\cos \vartheta$

$\vartheta$

0

0

0

−

0

$\frac{\pi }{2}$

1

1

1

1

$\frac{1}{2}$

$\frac{\pi }{3}$

1

−1

−1

1

$-\frac{1}{2}$

$\frac{2\pi }{3}$

2

2

2

2

$\frac{\sqrt{2}}{2}$

$\frac{\pi }{4}$

2

−2

−2

12

$-\frac{\sqrt{2}}{2}$

$\frac{3\pi }{4}$

3

3

3

3

$\frac{\sqrt{3}}{2}$

$\frac{\pi }{6}$

3

−3

−3

3

$-\frac{\sqrt{3}}{2}$

$\frac{5\pi }{6}$