Scalar and vectors (Mathematics)

Course Introduction: Scalars & Vectors Made Simple

Welcome to this comprehensive course on Scalars and Vectors, designed for students starting from the basics and progressing to more advanced concepts.

In this course, you will:

• Learn the definitions of scalars and vectors

• Understand their properties and basic operations

• Master how to find the magnitude and unit vector

• Explore operations like vector addition, subtraction, equal and zero vectors

• Work with position vectors and learn to find the direction of vectors

• Learn how to check if vectors are parallel, orthogonal (perpendicular), or equal

• Understand laws like the Triangle Law, Parallelogram Law, Commutative and Associative Laws of Addition

You’ll also study:

• Dot and Cross Products and their differences

• Their applications in daily life and physics

• Vectors in 2D and 3D, including how to transition from two to three dimensions

• The meaning of direction cosines and direction angles

• How to find the angle between two vectors

• Use dot and cross products to solve problems

• Learn to check whether vectors are coplanar

• Apply scalar triple products and find areas and volumes like those of parallelograms, parallelepipeds, and tetrahedrons

Throughout the course, you’ll practice with plenty of worked examples, problem-solving techniques, and step-by-step methods for tackling typical exam-style questions.

By the end, you’ll have a clear, practical understanding of vectors, their operations, and applications — ready to use in maths, physics, and engineering problems.