Scalar and vector quantities

Introduction to Scalar and Vector Quantities

  • A quantity in physics is something that can be measured. Quantities can be classified into scalars and vectors.
  • A scalar is a quantity that is completely described by a magnitude (size or amount) alone. Examples include: time, temperature, mass, distance, speed, energy, and electric charge.
  • A vector is a quantity that is fully described by both a magnitude and a direction. Examples include: displacement, velocity, acceleration, force, momentum, and weight.

Understanding Scalars

  • Scalars simply describe the magnitude of something, with no direction attached. The information provided by a scalar is wholly contained in its magnitude.
  • Scalar quantities can be added, subtracted, multiplied, or divided just like ordinary numbers. This forms the basis of scalar arithmetic. For example, when measuring distances, you can simply add two distances to find the total distance.

Understanding Vectors

  • Vectors are arrow-like objects used to represent quantities that have both magnitude and direction. They can be represented graphically or algebraically.
  • A graphical vector is drawn as an arrow, where the length of the arrow represents the magnitude of the vector and the direction of the arrow indicates the direction of the vector.
  • An algebraic vector is usually written in the format a = ai + bj + ck, where a, b, and c are real numbers and i, j, and k are unit vectors along the x, y, and z axes respectively. The numbers a, b, and c can also be known as components of the vector.
  • Vectors can be added or subtracted using the parallelogram rule or the triangle rule, and they can also be multiplied by scalars.
  • When multiplying a vector by a scalar quantity, the magnitude of the vector is multiplied, but the direction remains the same.

Vector Resolution

  • Sometimes it’s necessary to break down vectors into components, a process known as vector resolution.
  • The resolution of a vector into two perpendicular directions (like x and y) helps in dealing with vectors in a more systematic and organized manner.
  • The resolved parts or components of a vector are two vectors which together give the original vector.