Vectors
A pilot flies north at 200 kilometres an hour, but a wind pushes her east. Where does she end up? The answer needs both a size and a direction, and a number alone cannot give it. A vector does. This chapter builds the algebra of vectors in the plane and in space: how to add them, scale them and split them at a point. Then it gives two ways to multiply them, the dot product for angles, projections and work, and the cross product for areas and volumes. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP. Python checks every number.
Part of Mathematics · High School (11–12) (chapter 14)
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Vectors and Their Algebra
A ship sails 6 kilometres north and then 8 kilometres east. How far is it from the harbour? The distance sailed is one number, but where the ship is needs a size and a direction. In this course you describe a vector by its components and its direction cosines, add and scale vectors, and find the point that divides a line in a given ratio. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
The Dot Product
How much of a push along a ramp does a rope give when it pulls at an angle? Only the part of the force that points along the motion does the work. The dot product measures that part. In this course you find the dot product from components and from the angle. You use it to find angles and to test for right angles. Then you use it for projections and for work done. It covers the second part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.