priamky

Priamky are fundamental objects in Euclidean geometry. A priamka is the set of all points that lie on a single straight path, extending without bound in both directions and having no thickness. In two-dimensional space (the plane) or in three-dimensional space, a priamka is typically described as the line through two distinct points. A, B are points, and the line AB consists of all points collinear with A and B; through any two distinct points there passes exactly one line.

Lines can be represented in different forms. In a plane, the Cartesian equation of a line is ax + by + c = 0, with slope m = -a/b for b ≠ 0. If b = 0 the line is vertical. The slope-intercept form is y = mx + b, where m is the slope and b the y-intercept. In vector form, a line can be described parametrically as r(t) = p0 + t v, where p0 is a point on the line and v is a direction vector.

Two lines may be parallel (never meet), intersect (at a single point), or, in three dimensions, be skew (neither parallel nor intersect). The distance from a point to a line in the plane is |ax0 + by0 + c| / sqrt(a^2 + b^2).

Priamky are distinct from line segments, which have finite length between endpoints, and from rays, which start at a point and extend indefinitely in one direction. They form the foundational objects used to describe directions, angles, and intersections in geometry and related disciplines.

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