Vector Definition: Explaining Left Side to Right Side

[christian0710]

Hi For some strange reason I just can't see why this is true?? Can anyone help me explain why the left side can be written as the right side? I added a picture.

 

[christian0710]

The thing that confuses me the most is the p-tu.

 

[HallsofIvy]

It's just the associative law for addition of vectors:
(v- p)+ (p- tu)= v+ (-p+ p)- tu= v- tu.

 

[christian0710]

Ahh that's the trick huh? So is (v- p)+ (p- tu) a geometric figure? Or just something to be considered as numbers.