Vector shortcuts?

[Matt3122]

Hey,

Are there any shortcuts to remembering and doing the resolution of vectors? I'm always having issues trying to remember the formula 
so is there sort of an easier way of remembering it??

thx

[lzxnl]

Firstly, don't remember the formula if you don't understand it.

Whenever I forget, I use this method:
Assume you want vector resolute of a in the direction of b.
Then, you want some scalar k such that a-kb is perpendicular to b. This step is crucial. Do not read further until you understand this step.
You can then write (a-kb).b=0 =>a.b-kb.b=0=>k=a.b/b.b

So your "formula" is a.b/b.b b as the resolute


Secondly, when you're used to this formula, there's an easy way of remembering it. Notice how there are three b's in the fraction. That's because we're finding a resolute "in the direction of b". If it were in the direction of a, we would have a.b/a.a a. Do you see a pattern?