what is the difference between the standard unit vector and unit vector.In the book written by A.K.hazra, he says that "unit vector and standard unit vectors should not be confused. They are two different objects. A unit vector is expressible in terms of strandard unit vector but not the converse.thus unit vector $[3/4 \;\;\;\; 4/5 ]=\frac{3}{4}[1 \;\;\; 0] +\frac{4}{5}[0 \;\;\; 1 ] where\; [1\;\;\; 0]\; and \:[0\;\;\; 1 ]$? are standard unit vector. ".
now this is the question.what does the unit vector mean?According to my understanding unit vector is one whose magnitude is unity.so i cant understand his sayings.Finally what is the difference between the unit vector and standard unit vector.Is $[3/4 \;\;\;\; 4/5 ]$ is a unit vector?
Unit vectors are any vector $u$ where $\|u\| = 1$
The standard unit vectors are the unit vectors that are parallel to the coordinate axes. $i,j,k$ if you use that notation, or $(1,0,0), (0,1,0), (0,0,1)$ in $\mathbb R^3$ if you prefer.