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The scalar (dot) product a·b = |a||b|cos θ combines two vectors to give a number, and is zero when they are perpendicular. This topic covers calculating it from components and finding the angle between vectors. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Multiply the matching components and add them. The result is also the product of the two magnitudes and the cosine of the angle between, so rearranging gives the angle. A dot product of zero means the vectors are perpendicular.
Before you start
It draws heavily on vector notation and magnitude. Later work on angles between lines and perpendicularity assumes it. Examined in Pure 4.
What you learn
The scalar product (or dot product) of two vectors is a single number. It is the key to angles between vectors and lines, and to testing whether vectors are perpendicular. The angle between two lines is the angle between their direction vectors. To find an angle at a vertex of a figure, use the two vectors that point away from that vertex along the sides. The course works through the scalar (dot) product, the angle between two vectors, perpendicular vectors, the angle between two lines, angles inside geometric figures and problem solving with the dot product. 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
Scalar (Dot) Product is a Vectors topic in the A-level syllabus, covered here at the second year of A-level. It runs to 6 concepts, each followed by a check, with 6 worked examples along the way. Nearby topics in the same strand are Vector Equations of Lines, Angles & Geometric Problems and Parallel, Intersecting & Skew Lines . The Vectors revision engine gives you as many extra questions as you want, tracked on your skill tree.
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