What is a vector?

A vector is defined as a quantity that possesses both magnitude and direction. This is typically represented visually by an arrow, where the length of the arrow indicates the magnitude of the vector, and the orientation of the arrow indicates its direction. In various fields such as physics and engineering, vectors are essential for representing forces, velocities, displacements, and other directional quantities.

For instance, when describing the motion of an object, saying it is moving 10 meters to the east involves both how far it is moving (magnitude) and the direction (east). This duality is crucial for accurately describing and analyzing physical phenomena.

The other options do not fully encapsulate the definition of a vector. A quantity with magnitude only refers to a scalar, which lacks direction. A measurement of time focuses solely on temporal measurement and does not consider direction or magnitude in the context of vectors. A force applied to an object, while it can be a vector, does not define what a vector is as a whole, since not all vectors are forces. Thus, the complete definition of a vector is best captured by the representation of a line with an arrowhead that denotes both magnitude and direction.