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Mathematics

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Mathematics

M
Mithilesh Kumar Pande

30 Views • Apr 23, 2025

Wikipedia Context

Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in the natural sciences, engineering, technology, economics, and everyday life.

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Important Points to remember
The shortest distance between two skew lines is the line segment perpendicular to both lines.
If l, m, n are the direction cosines, and a, b, c are the direction ratios of the line, then the direction cosines are given by:




Skew lines are the lines that lie in different planes. They are neither parallel and nor intersecting.


The cartesian equation of a line that passes through the points (x1, y1, z1) and (x2, y2, z2) is given by




The equation of the plane that passes the three non-collinear points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) is



The equation of the plane which cuts the coordinate axes at (a, 0, 0), (0, b, 0) and (0, 0, C) is given by




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