HSC EV Higher Mathematics 1st Paper 3rd Chapter Note. Straight Lines. Coordinate Geometry is the unification of algebra and geometry in which algebra is used in the study of geometrical relations and geometrical figures are represented by means of equations. The most popular coordinate system is the rectangular Cartesian system. Coordinates of a point are the real variables associated in an order to describe its location in space. Here we consider the space to be two-dimensional. Through a point O referred to as the origin, we take two mutually perpendicular lines XOX’ and YOY’ and call them x and y-axes respectively. The position of a point is completely determined with reference to these axes by means of an ordered pair of real numbers (x, y) called the coordinates of P where |x | and | y | are the distances of the point P from the y-axis and the x-axis respectively, x is called the x-coordinate or the abscissa of P and y is called the y-coordinate or the ordinate of the point P.
HSC EV Higher Mathematics 1st Paper 3rd Chapter Note. Straight Lines
What is the general form of a pair of straight lines? What is the condition to find the equation represent a pair of straight lines? The formula to find the angle between a pair of straight lines. What is the condition to prove whether the pair straight lines are perpendicular or parallel? How to find the distance between them. How to find separate equations from the given pair of straight lines 123 Views · View Upvoters. Where can I download RD Sharma class 11 maths FREE? Is class 11 CBSE maths really very difficult? Which book is good for maths class 11? What book should I use in class 11 maths CBSE? Is CBSE class 11 and 12 maths tough? Is class 12 maths related to class 11? How is math in CBSE class 11 and 12? What are the passing criteria for maths in class 11? Is it important to score good marks in class 11? Is it important to pass in maths in class 9? What basics of maths are important for physics from class 11? How can I clear my basic concept of class 11?
Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and the determinant can be used to solve those equations, although more efficient techniques are actually used, some of which are determinant-revealing and consist of computationally effective ways of computing the determinant itself. The use of determinants in calculus includes the Jacobian determinant in the change of variables rule for integrals of functions of several variables. Determinants are also used to define the characteristic polynomial of a matrix, which is essential for eigenvalue problems in linear algebra. In analytic geometry, determinants express the signed n-dimensional volumes of n-dimensional paralleled. Sometimes, determinants are used merely as a compact notation for expressions that would otherwise be unwieldy to write down. When the entries of the matrix are taken from a field (like the real or complex numbers), it can be proven that any matrix has a unique inverse if and only if its determinant is nonzero. Various other theorems can be proved as well, including that the determinant of a product of matrices is always equal to the product of determinants; and, the determinant of a Hermitian matrix is always real.
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