You are Here: Home >< Maths

# Vectors and planes watch

Announcements
1. This should be really simple but I'm getting lost somewhere.

http://www.maths.leeds.ac.uk/~sergue...351/index.html

Then click handouts, then lecture notes and look at the problem at the bottom of Page 20, labelled (1.40) .

Looking at the bottom line, I understand the |BC| = |BA|cosθ part.
But then I would say,

|BC| = |a-b|cosθ

Can somebody explain why cosθ disappears and where the unit vector n comes from please?
2. You know that BA=a-b. So |BA|=|a-b|=|a-b||n|, since |n|=1 (because it's a unit vector).

Now, the dot product |P.Q| is defined as |P||Q|cosθ, where θ is the angle between P and Q. So |a-b||n|cosθ=|(a-b).n|.
3. Ah.. I see! Just to clear up though- usually, I'd define the dot product as,

p.q = |p||q|cos θ [i.e with no modulus], in which case,

|a-b||n|cosθ = (a-b).n

So I assume you just added the modulus to the (a-b).n term because it is a length, right?
4. Precisely. Since the dot product gives you a scalar quantity, the modulus signs basically have no bearing at all. What they do is ensure that you don't get a negative distance. (Although in some cases getting negative values might help point out which side of the plane the point is on.)
5. Thanks for clearing that up!
6. oh my gosh i should know this...should i be worried that i don't?!?!? lol its only been what? 3months since iv done this! aaaaaaaaaaaaaaargh thank god im nt doing a degree in maths!!!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: August 26, 2005
Today on TSR

### The Simpsons...

How would you end the show?

### University open days

• Sheffield Hallam University
Thu, 13 Dec '18
• University of Buckingham
Thu, 13 Dec '18
• University of Lincoln
Mini Open Day at the Brayford Campus Undergraduate
Wed, 19 Dec '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams