Courses

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.

StemPy Lab

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.

StemPy Lab

A wrench turns a bolt best when you push at right angles to the handle. The cross product captures this: it is a vector at right angles to both of its factors, and its size is the area of the parallelogram they span. In this course you use the right-hand rule and find areas of triangles and parallelograms. Then you use the scalar triple product for volumes, and for the test of whether four points lie in one plane. It covers the last part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level Further Maths, IB Higher Level and AP.

StemPy Lab