Mathematics
High School (11–12)
Vectors and Three-Dimensional Geometry › Three-Dimensional GeometryChapter 15Contains Standard contentThree-Dimensional Geometry
Two aeroplanes fly in the same sky. Will they meet, or only seem to cross? A drone lands on a sloping roof. How far was it from the roof a moment ago? These questions live in three dimensions, and the answers come from lines and planes written as equations. In this chapter you describe a line by its direction and one point, find the angle between lines, measure the shortest distance between lines that never meet, and then do the same for planes. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level Further Maths and IB. Python checks every answer on the computer.
Part of Mathematics · High School (11–12) (chapter 15)
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Lines in Space: Direction Cosines, Equations and Angles
How do you tell a friend which way a kite string runs? You give a direction, and in space a direction needs three numbers. Learn direction cosines and direction ratios, write the equation of a line in vector and Cartesian form, and find the angle between two lines. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level Further Maths and IB.
Skew Lines and Shortest Distances
Two cables hang across a street at different heights. They do not touch, and they are not parallel. How close do they come? Such lines are called skew, and they exist only in space. Test whether two lines meet, find the shortest distance between two lines, and find the distance of a point from a line together with the foot of the perpendicular. It covers the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level Further Maths and IB.