data <- data.frame(structure(list(Pt = c(1L, 2L, 4L, 15L, 16L, 28L), X_Pos = c(721581.7113, 720696.7993, 721964.1754, 722729.8494, 721124.2707, 722907.4276
+ ), Y_Pos = c(4392224.808, 4391486.166, 4392769.078, 4391677.301,  4390212.733, 4387364.466), Z_Pos = c(3895.530029, 3857.147705, 3914.577148, 4171.714355, 4057.708008, 4568.308105), X3dresidual = c(1.09432, 2.8117, 3.771, 2.96983, 3.771, 1.2507), vec_x = c(0.0128787, -1.72378, 0.706588, 1.93419, -0.764626, -0.27738), vec_y = c(1.00485, 1.2046, -0.345822, -0.626616, 1.30789, -0.552963), vec_z = c(-0.433178, 1.86633, -1.50366, 2.16476, -3.4532, -1.08699)), .Names = c("Pt","X_Pos", "Y_Pos", "Z_Pos", "X3dresidual", "vec_x", "vec_y", "vec_z"), class = "data.frame", row.names = c(NA, -6L)))


  Pt    X_Pos   Y_Pos    Z_Pos X3dresidual      vec_x     vec_y     vec_z
1  1 721581.7 4392225 3895.530     1.09432  0.0128787  1.004850 -0.433178
2  2 720696.8 4391486 3857.148     2.81170 -1.7237800  1.204600  1.866330
3  4 721964.2 4392769 3914.577     3.77100  0.7065880 -0.345822 -1.503660
4 15 722729.8 4391677 4171.714     2.96983  1.9341900 -0.626616  2.164760
5 16 721124.3 4390213 4057.708     3.77100 -0.7646260  1.307890 -3.453200
6 28 722907.4 4387364 4568.308     1.25070 -0.2773800 -0.552963 -1.086990