I noticed that a lot of students have problems with H2 maths Vectors, with all the finding of shortest distance between line and plane, between point and line, etc. So I'm going to share with you what I think is the right way to study, prepare and understand the topic of vectors.
The thing is, there is no need to memorise all the formulae! They will kill you if you use and apply it blindly. You are more likely to careless, especially when trigo is involved. You might get the angle wrongly, etc etc. And so many formulae will make you go bonkers; you still have other topics (and subjects) to take care of. What AB dot unit vector n, AB cross unit vector n, etc... will decimate you in no time when you have to handle all the subjects.
The key thing, as my students would know, is to make full use of your power and concept of trigonometry (O levels sufficient) as well as the basic and fundamental things you learned about vectors. I myself cannot remember any formulae off-hand for finding shortest distance, but from trigo concept, I can always come up with the equation in about 2 to 3 steps. Not much extra to use in exams, considering that you save a lot of brain capacity for other topics.
How do go about doing this?
Look through your notes again. Your teachers should have given you notes on how to arrive at the shortest distance equations by derivation. Try to understand how they come about, and with that understanding, do your tutorials and practices with it. Then you will still most likely be able to do A levels vectors question many years after you finish A levels with basic O level trigo.
Hi,
I agree with eagle.
Essentially, almost all results in vectors come from two basic definitions (both involve trigonometry):
1. a.b = |a| |b| cos theta
2. |a x b| = |a| |b| sin theta
Please refer to my website for details:
http://www.freewebs.com/weews/scalarproduct.htm
http://www.freewebs.com/weews/vectorproduct.htm
Thanks!
Cheers,
Wen Shih