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This vectors topic uses the scalar (dot) product and vector methods to find angles between lines and vectors and to solve geometric problems in two and three dimensions. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Form vectors between the points, taking care with direction, then use the dot product for angles and magnitudes for lengths. Sketching the situation first stops you finding the angle between the wrong pair.
Before you start
Bring the scalar product and vector lines with you. It is Pure 4 content. This is the foundation for 3D problem solving.
What you learn
The course works through the foot of the perpendicular from a point to a line, the shortest distance from a point to a line, the area of a triangle, the area of a parallelogram, geometric configurations and proofs and bringing it together. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Angles & Geometric Problems is part of the Vectors strand of our free A-level maths courses, studied in the second year of A-level. It runs to 6 concepts, each followed by a check, with 6 worked examples along the way. Related topics students usually take next include Parallel, Intersecting & Skew Lines , Scalar (Dot) Product and Vector Equations of Lines. The Vectors revision engine gives you as many extra questions as you want, tracked on your skill tree.
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