Lines and planes in space

Section Formulae

A line segment could be divided into two parts by placing a point on the line between the two extreme ends of the line segment or someplace outside of the line segment. Section formulas can also be used in coordinate geometry to determine a relationship between the coordinates of the point that divides a line […]

Section Formulae Read More »

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

Scalar Triple Product

A dot product of a vector also with cross product of two additional vectors is called the scalar triple product. For example, if a, b, and c are three vectors, the scalar triple product is a .(b x c). The  scalar triple product, box product, & mixed product are other names for it. The volume

Scalar Triple Product Read More »

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

Scalar Triple Product

Introduction Have you ever gotten stuck when trying to solve a scalar triple product problem? If you have, don’t worry. In this article, we will show you how to solve any scalar triple product problem. The answers to these problems are derived from the volume of the parallelepiped having every three vectors as its sides

Scalar Triple Product Read More »

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

Rotational symmetry

It is explained by the rotational symmetry of a shape, which states that when an object is rotated about its own axis, the shape of the object remains unchanged. Many geometrical objects appear to be symmetrical when they are rotated 180 degrees or with certain angles, either clockwise or anticlockwise, in the same direction. Some

Rotational symmetry Read More »

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

Rotation

When we talk about rotation in mathematics, we are talking about a transformation that revolves around a figure around a fixed point known as the centre of rotation. In rotation, there is a fixed point at the centre of the circle, and everything else revolves around that point as it rotates. With another way of

Rotation Read More »

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

Rhombus And Parallelogram

Introduction A quadrilateral is a four-sided polygon in the field of geometry. The different quadrilaterals are the square, rectangle, rhombus, parallelogram, kite, and trapezium, all of which have some traits in common with one another. It is well known that the rhombus and the parallelogram are both termed quadrilaterals due to the fact that they

Rhombus And Parallelogram Read More »

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

Reverse Triangle Inequality

In mathematics, an inequality known as the triangle inequality asserts that the total of the lengths of any two sides of a triangle must be more than or equal to the length of the third side of the triangle. This rule applies to any triangle. This statement allows for the inclusion of degenerate triangles; however,

Reverse Triangle Inequality Read More »

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

Relationship Between Measure Theory and Carathéodory theorem

Any pre-measure defined on a given ring R of subsets of a given set can be extended to a measure on the -algebra generated by R, and this extension is unique if the pre-measure is -finite, according to Carathéodory’s extension theorem, which was named after the mathematician Constantin Carathéodory.  This theorem is part of measure

Relationship Between Measure Theory and Carathéodory theorem Read More »

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

Relation Between the Direction Cosines of a Line

The cosines of the angles formed by a (directed) line with the positive directions of the coordinate axes are called direction cosines. Consider the following line OL, which passes through the origin O. Allow OL to be angled away from the coordinate axes. –l, –m, and –n are the direction cosines for the line LO

Relation Between the Direction Cosines of a Line Read More »

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