Question 980957
<pre>
Here is a picture of the vector <3,4>. A vector is an arrow.
It has a tip and a tail.  It can be located anywhere.  The
green line is 3 units long.  It represents the first component 
3 and the red line indicates its y-component 4.  The angle <font face="symbol">q</font>
is the direction of the vector.


{{{drawing(300,300,1,9,1,9,grid(1), 
red(arc(3,2,1.5,-1.5,0,54)),locate(3.3,2.4,theta),
green(line(3,2,6,2)), red(line(6,2,6,6)),
line(3,2,6,6), line(5.91626933,5.30502577,6,6), line(5.35626933,5.72502577,6,6)
)}}}

Its direction is inverse tangent of 4/3 or 53.13° North of East.

Its magnitude is found by the Pythagorean theorem:

Its magnitude is the length of the arrow, or
 
{{{sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5}}}

Edwin</pre>