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Dec 21, 2020 · Unlike a plane, a line in three dimensions does have an obvious direction, namely, the direction of any vector parallel to it. In fact a line can be defined and uniquely identified by providing one point on the line and a vector parallel to the line (in one of two possible directions).
Aug 12, 2022 · Two points on a plane determine a line. A line is a one-dimensional figure that is made up of an infinite number of individual points placed side by side. In geometry, all lines are assumed to be straight; if they bend they are called a curve. A line continues infinitely in two directions.
Aug 13, 2024 · This chapter discusses the definitions and examples of point, line, ray, line segment and a plane. How two or more than two lines can make when meet at some point for example intersecting lines, perpendicular lines, parallel lines, transversal lines and concurrent lines with the help of diagrams.
- Points, Lines, and Planes in Geometry
- What Is A Point?
- Collinear and Non-Collinear Points
- Coplanar and Non-Coplanar Points
- What Is A Line?
- Line Segment
- Mid-Point
- Rays
- Intersecting and Parallel Lines
- Perpendicular Lines
In basic geometry, fundamental concepts like points, lines, and planes form the foundation upon which more complex geometric ideas are built. Points are precise locations in space, devoid of size or dimension, represented simply by dots. Lines are infinite paths stretching in two opposite directions, composed of an unending series of points. They a...
A Point in geometry is defined as a location in the space that is uniquely determined by an ordered triplet (x, y, z) where x, y, & z are the distances of the point from the X-axis, Y-axis, and Z-axis respectively in the 3-Dimensions and is defined by ordered pair (x, y) in the 2-Dimensions where, x and y are the distances of the point from the X-a...
When 3 or more points are present on the straight line then such types of points as known as Collinear pointsand if these points do not present on the same line, then such types of points are known as non-collinear points.
When the group of points is present on the same plane then such types of points are known as coplanar points and if these points do not present on the same plane, then such types of points are known as non-coplanar points.
A Line in three-dimensional geometry is defined as a set of points in 3D that extends infinitely in both directions It is the smallest distance between any two points either in 2-D or 3-D space. We represent a line with L and in 3-D space, a line is given using the equation, In 3D we can also form a line by the intersection of two non-parallel plan...
A line segment is defined as the finite length of the line that is used to join two points in 2-D and 3-D. It is the shortest distance between two points. A line segment between two points A and B is denoted as, AB A line has infinite length whereas a line segment is a part of a line and has finite length.
Midpointis defined as the point on the line segment which divides the line segment into two equal parts. Suppose we have two points A and B and the line segment joining these two points is AB and not the point P on the line is called the midpoint if it breaks the line into two equal parts such that, AP = PB Thus, P is called the midpoint of line se...
A ray is defined as a line that has a fixed end point in one direction but can be extended to infinity in the other direction. It is of infinite length. We define the ray joining points O and A and extending to infinity towards A as
In 2-D any two lines can either meet at some point or they never meet at some point. The lines that meet at some point are called intersecting lines. The distance between the intersecting line keeps on decreasing as we move toward the point of intersection, and at the point of intersection of these lines, the distance between them becomes zero. Whe...
Intersecting lines that intersect at right angles are called perpendicular lines. The angle between theseperpendicular linesis always the right angle or 90 degrees. The perpendicular lines are shown in the image added below:
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In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc. In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also.
- There are many shapes in geometry based on their dimensions. Circle, Triangle, Square, Rectangle, Kite, Trapezium, Parallelogram, Rhombus and diff...
- There are basically six types of triangles: Scalene Triangle Isosceles Triangle Equilateral Triangle Acute-angled triangle Obtuse-angled trian...
- The basic polygons are: Triangle Quadrilaterals – square, rectangle, parallelogram, trapezium, kite Pentagon Hexagon Heptagon Octagon Nonago...
- Cube – Sugar cube, Rubik’s cube Cuboid- A wooden rectangular box, matchbox Cone- Icecream cone, Pyramid Sphere- Football, Basketball Cylinder-...
- The basic solid shapes are Cube, Cuboid, Cone, Sphere, Hemisphere and Cylinder.
We can draw certain figures like square, rectangle, triangle, and circle on the plane. Hence, these figures are also called plane figures. Incidence Properties of Lines in a Plane: An infinite number of many lines can be drawn to pass through a given point in a plane.
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While there are many normal vectors to a given plane, they are all parallel or anti-parallel to each other. Suppose two points \((v_1,v_2,v_3)\) and \((w_1,w_2,w_3)\) are in a plane; then the vector \(\langle w_1-v_1,w_2-v_2,w_3-v_3\rangle\) is parallel to the plane.
