Vectors

Introduction to Vectors

  • Become familiar with the concept of a vector as a quantity described by magnitude (size) and direction.
  • Understand that vectors differ from scalars which only have magnitude, lacking any directional component.
  • Recognise vector notation, with vectors typically represented by boldface letters (e.g., v) or letters with arrows above them.

Basic Calculations and Concepts

  • Learn to perform basic vector operations, including addition (resultant), subtraction and multiplication (both scalar and vector product).
  • Understand how to express vectors in terms of unit vectors i, j, k corresponding to x, y and z axis respectively.
  • Familiarise with the geometric representation of vectors, and how to calculate the magnitude (length) and direction of a vector.

Vector Resolution and Components

  • Understand the concepts of vector resolution - resolving a vector into its horizontal and vertical components.
  • Learn to calculate the components of a vector and comprehend the part each component plays in determining the overall vector.

Scalar and Vector Products

  • Become proficient in calculating the dot product (also known as the scalar product), which combines two vectors to produce a scalar.
  • Master the cross product (also known as the vector product), which combines two vectors to produce a third vector, perpendicular to the initial two.

Vector Applications in Physics

  • Understand the significance of vectors in various branches of physics like Mechanics, wherein the forces, velocity and acceleration are represented as vectors.
  • Explore implications of vectors in relative velocity problems and become comfortable with addition or subtraction of vectors in such scenarios.

Practice Questions and Problem Solving

  • Regularly attempt problems involving vectors, ranging from basic operations to more complex questions involving resolution and applications in physics.
  • Utilise worked examples to consolidate understanding and ensure to re-do problems independently.
  • Persevere when solving vector problems to improve problem-solving skills and increase confidence.