Vector Solutions, Shortcuts, Formulas

Vector Video Lecture - Page 9

Some Basic Concept of Vector: Let l be any straight line in plane or three dimensional space. This line can be given two directions by means of arrowheads. A line with one of these directions prescribed is called a directed line {Fig 10.1 (i), (ii)}. Now observe that if we restrict the line l to the line segment AB, then a magnitude is prescribed on the line l with one of the two directions, so that we obtain a directed line segment {Fig 10.1(iii)}. Thus, a directed line segment has magnitude as well as direction.

Definition: A quantity that has magnitude as well as direction is called a vector .

Notice: That a directed line segment is a vector fig {10.1(iii)}, denoted by as $\vec{AB}$ or simply as $\vec{a}$ , and read a ‘ vector $\vec{AB}$’ or ‘vector $\vec{a}$’.

The point A from where the vector $\vec{AB}$’ starts is called its initial point , and the point B where it ends is called its terminal point. The distance between initial and terminal points of a vector is called the magnitude (or length) of the vector, denoted as $|\vec{AB}|\: or\: |\vec{a}|$ , or a .The arrow indicates the direction of the vector.