Some physical quantities make sense with their size (magnitude) alone (e. g. height of a person). However, some physical quantities needs a direction to make complete sense (e. g. position of a ship). This feature enables categorizing physical quantities into two groups as vectors and scalars. A scalar quantity needs only a magnitude to report its status. A vector quantity requires a direction, in addition to magnitude, to report its status. Vector Notation
In reporting and recording, a vector quantity is distinguished from a scalar quantity by denoting an arrow (usually to the right) above the quantity notation. indicates that the quantity denoted by For example, ~ A A is a vector quantity.
The Magnitude of a Vector Magnitude refers to the size (measure) of the vector quantity The magnitude is given in terms of a standard size (unit). The vector notation between vertical bars (||) indicates the magnitude of a vector. For example, ~ means the magnitude of A ~. |A| Sometimes the quantity notation is used without the arrow (A) to indicate magnitude. However, let us consistently use || notation for the magnitude of a vector to make it easy to distinguish between a scalar ~ ). A), a vector quantity (A~ ), and the magnitude of a vector quantity (|A| quantity
The Direction of a Vector The direction of a vector species the angle a vector makes with a xed direction. For 0 example, wind blows at 36 m/s along 30 towards West from North completely specify a 0 vector in its magnitude (36 m/s) and direction (along 30 towards West from North).
Some physical quantities are vectors, and being vectors they each MUST have a magnitude and a direction. Also we know that every physical quantity have dimensions . Where in the vector (in the magnitude, in the direction, or in both) the dimensions are recorded? Explain!
Physical quantities are either vectors or scalars.
What kind of quantities qualify to become scalars (real numbers, positive quantities only, negative quantities only, both)? Explain.