Vectors and Scalars
Distinction between scalar and vector quantities, geometric addition, parallelogram and triangle laws, and resolution of vectors into perpendicular components.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Categorize physical quantities as vectors or scalars based on magnitude, direction, and vector transformation laws.
- Resolve vectors along mutually perpendicular axes to determine resultant vectors analytically.
Core Theory & Concepts
Vectors and Scalars form the mathematical cornerstone of classical mechanics. Forces, velocities, displacements, and momenta possess essential spatial directions that must be combined using vector geometry rather than ordinary scalar arithmetic.
Rectangular Resolution
Any vector A inclined at angle θ to the horizontal resolves into perpendicular components: A_x = A cos θ and A_y = A sin θ. The original vector magnitude is restored by Pythagoras: A = √(A_x² + A_y²).
Parallelogram Law of Addition
The resultant of two forces P and Q acting at angle θ is given by the diagonal of the parallelogram: R = √(P² + Q² + 2PQ cos θ).
Common Misconceptions
Assuming electric current is a vector because it has a direction along a wire.
Syllabus Topic Outline
- 1Scalars versus vectors definition and distinction
- 2Vector addition and subtraction laws (Triangle and Parallelogram)
- 3Resolution of vectors into rectangular components
- 4Resultant of coplanar concurrent vectors
Interactive 2D Vector Workspace
Geometric representation, rectangular component resolution, addition, subtraction & polygon law