Chapter 9.4, Problem 96AYU

To determine

To explain: the difference between algebraic vector and position vector.

Explanation of Solution

A vector is a line segment oriented from an initial point to a final point. ... Algebraic vectors are related to a coordinate system, and include subcategories: Position vector, which connects the origin of the coordinate system with any point. Displacement vector, which connects two different points.

Algebraic - Treats a vector as set of scalar values as a single entity with addition, subtraction and scalar multiplication which operate on the whole vector. Geometric - A vector represents a quantity with both magnitude and direction.

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P. In other words, it is the displacement or translation that maps the origin to P:

A vector that starts from the origin (O) is called a position vector.