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.

 

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