A scalar is a quantity that is determined by its magnitude.

Scalars and Vectors

Definition 8.1

A **scalar**** **is a quantity that is determined by its magnitude.

For instance, distance, length, speed, temperature, voltage, mass, pressure, and work are scalars.

Definition 8.2

A vector is a quantity that is determined by both its magnitude and its direction and hence it is a directed line segment.

For instance, force, displacement, and velocity (which gives the speed and direction of the motion) are vectors.

We denote vectors by lower case letters with arrow. A two dimensional vector is a directed line segment in R2 and a three dimensional vector is a directed line segment in R3.

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11th Mathematics : UNIT 8 : Vector Algebra I : Scalars and Vectors | Definition

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