Vectors in the Plane and in Space

Abstract

In physics certain quantities such as force, displacement, velocity, and acceleration possess both a magnitude and a direction and they are most usually represented geometrically by drawing an arrow with the magnitude and direction of the quantity in question. Physicists refer to the arrow as a vector, and call the quantity so represented a vector quantity. In the study of the calculus the student has no doubt also encountered what are called vectors, particularly in connection with the study of lines and planes and the differential geometry of space curves. We begin by reviewing these ideas and codifying the algebra of vectors.