i^, j^ and k^. Here i^ is the unit vector along x – axis, j^ is the unit vector along y – axis and k^ is the unit vector along z – axis. For instance, if force on a body is represented by expression 4i^ then indicates that magnitude of force is 4 N and it is acting along x – axis that is the direction of force is along x – axis. Magnitude of unit vector is always one (‘1’).
Unit vector of any vector A -> = a1 i^ + a2 j^ + a3 k^ will be given by Ratio of vector to magnitude of vector. This is shown below.
u^ = (A->) / │(A->)│,
Normal vector can be defined as unit vector which is normal to surface for which it is defined.
Let’s consider the following diagram for which Normal Vector can be defined. Let’s consider the following diagram for which the normal vector can be defined.
Here in above diagram, when vector A-> will be rotated towards vector B->, then according to right hand rule, direction will be normal to the surface. This normal direction is represented by a vector known as normal vector and it is denoted by ‘n^’. Here if vector A-> and vector B-> are in X-Y plane then direction of rotation will be along z – axis. Let’s derive the formula to find the unit vector with positive component which is normal to the surface.
Here normal vector can be found by cross multiplication of A-> and B-> as shown below:
A->* B->= │A->││* B->│sin x n^
And hence normal vector will be given by
n^ = (A->* B->) / │A->││* B->│sin x.