## Unit Vectors

Instead of explicitly writing A

_{x}= 5, A_{y}= 0; B_{x}= 5, B_{y}= 5; C_{x}= - 10, C_{y}= 0; and D_{x}= - 5, D_{y}= 5, we can write this same information in a different form. We can write

A= 5i+ 0j

B= 5i+ 5j

C= - 10i+ 0j

D= - 5i+ 5j

iandjare "unit vectors" in the x- and y-directions. Being "unit vectors", they each have a magnitude ofone. They carry only the direction information.Now we can write

R = A + B + C + D

R =(5i+ 0j) + (5i+ 5j) + (- 10i+ 0j) + (- 5i+ 5j)

R= ( 5 + 5 - 10 - 5 )i+ ( 0 + 5 + 0 + 5 )j

R= - 5i+ 10jNow we know the components of the resultant,

R

_{x}= - 5and

R

_{y}= 10and we can proceed exactly as before to recombine those to find the magnitude and the direction.

To explicitly remind ourselves that

iandjare "unit vectors", they are sometimes (or oftentimes) written with a "hat" or "caret" above them,

(c) Doug Davis, 2001; all rights reserved