Why does x1i =r1 -y1j in Lorentz electromagnetic force?

[retupmoc]

When going over my notes on the lorentz electromagnetic force in my physics 3 electromagnetism class got a bit puzzled by one statement that seems just to be taken for granted. Could anyone help me and tell me why x1i =r1 -y1j on page 5 on http://www.physics.gla.ac.uk/~dland/ELMAG305/Elmag305txt1.pdf where frame 1 is the stationary frame and 2 the frame moving with velocity v to the right of frame 1

If its just by using pythagorus wouldn't the above quantities (x,y and r) be to the second power. i just can't get my head around this and realize its probably something really straight forward. any help would be much appreciated.

 

[Integral]

the vector r = xi + yj by definition, see the figure on the previous page.

Using the Pythograean theorem you get the magnetude of r.

[tex] \mid \hat {r} \mid = \sqrt { x^2 + y^2 } [/tex]

You are dealing with the VECTOR r. See the difference?

 

[retupmoc]

haha yeah i do now and realize how obvious that was, thanks

 

[retupmoc]

Another quick question, why on page 6 of the slide does vy1k = v x r?