Lines and planes in space

Pair of Lines

In Geometry, we begin our study of shapes with a focus on lines because they are the most fundamental. When several lines meet in specific places and orientations, nearly all of the shapes that can be made can be described as “formed.” In this chapter, we will study everything there is to know about a […]

Pair of Lines Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

Orthogonal Trajectory

An orthogonal trajectory of the family is a curve that cuts every member of a particular family of curves at right angles. It is not required for the curve to pass through each family member. When they cross, however, the angle formed by their tangents at each point of intersection is 90°. Definition A curve

Orthogonal Trajectory Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

Orthocentre

The point of intersection of altitudes drawn perpendicular from the vertex to the opposing sides of a triangle is known as an orthocenter. The orthocenter of a triangle is the point at where the triangle’s three altitudes intersect. The following are the three most important aspects of an orthocenter. The center of all right angles

Orthocentre Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

Orthocentre

The point of intersection of altitudes drawn perpendicular from the vertex to the opposing sides of a triangle is known as an orthocenter. The orthocenter of a triangle is the point at where the triangle’s three altitudes intersect. The following are the three most important aspects of an orthocenter. The center of all right angles

Orthocentre Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

Obtuse angled triangle

A triangle is a two-dimensional plane figure with three sides and three angles that is closed in two dimensions. When the sides and interior angles of a triangle are taken into consideration, a variety of different types of triangles are formed, with the obtuse-angled triangle being one of them. When one of the interior angles

Obtuse angled triangle Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

Notes and Formulas about Three Dimensional Geometry

3D geometry is the study of shapes in three-dimensional space using three coordinates: x-coordinate, y-coordinate, and z-coordinate. To discover the exact location of a point in three dimensions, three criteria are necessary. A coordinate system is the technique of determining the position or location of a point on the coordinate plane in three dimensions. Important

Notes and Formulas about Three Dimensional Geometry Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

Normal Form of a Plane

While learning 3D Geometry, a line and a plane are two basic terms that can be defined. A line can be determined uniquely under two conditions when it passes through a point and has a direction or passes through two different points. A plane can be identified as a plane under three conditions.  The first

Normal Form of a Plane Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

NONAGON

Different forms of polygons can be found in geometry, as indicated in the diagram below. Based on the number of sides and angles, each of these polygons has different features.  A triangle is a 3-sided polygon, a quadrilateral is a 4-sided polygon, a 5-sided polygon is a pentagon, a 6-sided polygon is a hexagon, a

NONAGON Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry

Metric System

The metric system of measurement is the standard method for measuring distance, height, and most other everyday things. Consider a container of milk as an example. We measure the volume of milk in litres and the height of the jar in metres (or centimetres). This is due to the fact that these metric units, known

Metric System Read More »

Class 12, IIT JEE, Lines and planes in space, Maths, Three-Dimensional Geometry