content_image/309506.jpg content_image/309505.jpg content_image/309507.jpg content_image/309508.jpg content_image/309509.jpg content_image/309510.jpg
where 

If r = r ( s ) is a timelike curve, then above equations are given as [7] 

<img src='content_image/309506.jpg'>

The norm of a vector X is defined by [5] 

Theorem 1 : Let X and Y be non-zero orthogonal Lorentz vectors in R 3 $_{1}$. If X is timelike, then Y is spacelike [8]. 

Theorem 2 : Let X and Y be positive (negative ) timelike vectors in R 3 $_{1}$. Then 

with equality if and only if X and Y are linearly dependent [8]. 

Let X and Y be positive (negative ) timelike vectors in R 3 $_{1}$. Then there is a unique non-negative real number ϕ ( X, Y ) such that 

the Lorentzian timelike angle between X and Y is defined to be ϕ ( X, Y ) [8]. 

Let X and Y be spacelike vectors in R 3 1 that span a spacelike vector subspace. Then we have 

with equality if and only if X and Y are linearly dependent. Hence, there is a 

<img src='content_image/309505.jpg'>

<img src='content_image/309507.jpg'>

<img src='content_image/309508.jpg'>

<img src='content_image/309509.jpg'>

<img src='content_image/309510.jpg'>

