ε = { +1 , B is spacelike, − 1 , B is timelike. · T ( s ) = κ ( s ) N ( s ) , · N ( s ) = κ ( s ) T ( s ) − τ ( s ) B ( s ) , · B ( s ) = τ ( s ) N ( s ) . ‖ X ‖$_{IL}$ = √ |〈 X, X 〉| . 〈 X, Y 〉 ≤ ‖ X ‖ ‖ Y ‖ 〈 X, Y 〉 = ‖ X ‖ ‖ Y ‖ cosh ϕ ( X, Y ) |〈 X, Y 〉| ≤ ‖ X ‖ ‖ Y ‖ 4 where If r = r ( s ) is a timelike curve, then above equations are given as [7] 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 Let X and Y be spacelike vectors in R 3 1 that span a spacelike vector subspace. Then we have the Lorentzian timelike angle between X and Y is defined to be ϕ ( X, Y ) [8]. with equality if and only if X and Y are linearly dependent. Hence, there is a