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For 5-shot groups, based on 95% confidence, a rifle that normally shoots 1 MOA can be expected to shoot groups between 0.58 MOA and 1.47 MOA, although the majority of these groups will be under 1 MOA. What this means in practice is if a rifle that shoots 1-inch groups on average at 100 yards shoots a group measuring 0.7 inches followed by a ...
The vector projection of a on b is a vector a 1 which is either null or parallel to b. More exactly: a 1 = 0 if θ = 90°, a 1 and b have the same direction if 0° ≤ θ < 90°, a 1 and b have opposite directions if 90° < θ ≤ 180°.
Also, let Q = (x 1, y 1) be any point on this line and n the vector (a, b) starting at point Q. The vector n is perpendicular to the line, and the distance d from point P to the line is equal to the length of the orthogonal projection of on n. The length of this projection is given by:
Focal length can be calculated for the system in fig. 1 using the geometry shown in fig. 2 where it can be seen that changing the gap between the components (d+D in the figure) or the radius of curvature (R) will have a large effect on the focal length. Fig. 2- Geometry of MOA in configuration shown in fig. 1
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
If we condense the skew entries into a vector, (x,y,z), then we produce a 90° rotation around the x-axis for (1, 0, 0), around the y-axis for (0, 1, 0), and around the z-axis for (0, 0, 1). The 180° rotations are just out of reach; for, in the limit as x → ∞ , ( x , 0, 0) does approach a 180° rotation around the x axis, and similarly for ...
Any point above the x-axis is displaced to the right (increasing x) if m > 0, and to the left if m < 0. Points below the x -axis move in the opposite direction, while points on the axis stay fixed. Straight lines parallel to the x -axis remain where they are, while all other lines are turned (by various angles) about the point where they cross ...
Now the problem has become one of finding the nearest point on this plane to the origin, and its distance from the origin. The point on the plane in terms of the original coordinates can be found from this point using the above relationships between and , between and , and between and ; the distance in terms of the original coordinates is the ...