Vector and Scalar Quantities

Learning Objectives After completing this lesson you will be able to: Define the following terms: vector quantity, scalar quantity, resultant vector, equivalent vectors, collinear vectors. Distinguish between vector and scalar quantities using examples. Demonstrate an understanding of vector addition, a resultant vector and resolving a vector into components. Represent vector quantities on neat, accurate scale diagrams. Identify collinear and non-collinear vectors. Identify equivalent vectors. Add two or more collinear vectors and non-collinear mathematically and graphically to determine the resultant vector. Solve problems involving collinear and non-collinear vectors.

Key Concepts Scalar quantities consist of only a magnitude. Vector quantities consist of both a magnitude and direction and can be represented by a vector. The direction of a vector is stated using square brackets behind its magnitude. A vector is a line segment, drawn to scale, with an arrowhead indicating direction. The tail of a vector is called the origin and the tip or arrowhead is called the terminal point. Vectors can be collinear. A special type of collinear vector is an equivalent vector. Vectors can be non-collinear. They are vectors that exist in more than one dimension. Collinear vectors may be added algebraically or graphically using the tail-to-tip method. The sum of two or more vectors is called the resultant vector. Non-collinear vectors can be added mathematically (Pythagorean Theorem, vector component method, Sine and Cosine Laws) to determine the resultant vector.