Розрахунок: lbIP2l - 1

cos(α) =

( x1* x2+ y1* y2+ z1* z2)

/ ( saknis(

x1^²+ y1^²+ z1^²)* saknis(

x2^²+ y2^²+ z2^²))

cos(α) =

( x1* x2+ y1* y2+ z1* z2)

/ ( saknis(

x1^²+ y1^²+ z1^²)* saknis(

x2^²+ y2^²+ z2^²))

cos(\alpha)

=

\frac{x1\cdot x2+y1\cdot y2+z1\cdot z2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}

cos(α) =

x1* x2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

+

y1* y2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

+

z1* z2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

cos(\alpha)

=

\frac{x1\cdot x2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}+\frac{y1\cdot y2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}+\frac{z1\cdot z2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}

α = arccos((

x1* x2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

+

y1* y2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

+

z1* z2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

))

\alpha

=

arccos((\frac{x1\cdot x2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}+\frac{y1\cdot y2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}+\frac{z1\cdot z2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}))

α = arccos(

x1* x2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

+

y1* y2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

+

z1* z2

/ saknis(

x1^²+ y1^²+ z1^²)/ saknis(

x2^²+ y2^²+ z2^²)

)

\alpha

=

arccos(\frac{x1\cdot x2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}+\frac{y1\cdot y2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}}+\frac{z1\cdot z2}{\sqrt {x1^{2}+y1^{2}+z1^{2}}\cdot \sqrt {x2^{2}+y2^{2}+z2^{2}}})