Assumed knowledge of Vector Parlance

[rowshan]

navigating" a specialist question is hard, but when confronted with specific words like "concurrent" or "collinear" "coplanar", the question become impossible to solve.
Especially when they ask you to prove this something is "concurrent" or "collinear" "coplanar" and you don't know what the hell they mean.
Could someone please provide me with an easy to understand definition of the above words, maybe even a geometric representation and any other words that we should be aware of, and show a possible way to prove it too.
Cheers. =)

[cara.mel]

Collinear - can put 3 or more points in a straight line (note that if you only have 2 points you can always draw a straight line between them)
Coplanar - similar deal but points lie in the same plane

concurrent - I can't define this off the top of my head but I'd recognise its meaning in context

Someone else should come and give far better definitions though

[Glockmeister]

http://en.wikipedia.org/wiki/Concurrent_lines

[shinny]

So lemme clarify; to prove collinearity for the POINTS a, b, c, you'd have to prove the vectors AB=BC? Whilst for linear dependence, you have to prove for the VECTORS (position vectors) a,b,c that OA=mOB+nOC, m,n constants? I always get these two mixed up =S

[phagist_]

For collinear its AB=kBC.. where k is some real number

[shinny]

Oh whoops yeh, forgot the constant =\ AB=BC is to prove B is the midpoint of A and C i guess

[rowshan]

is that it for collinear? Easy enough. What about the rest?

[Mao]

to prove for collinear, as we've already said, we have to show that three points lie on the same straight line. i.e. AB = k BC, for some real k

to prove linear dependence (or independence) of three vectors, we have to show that a = m b + n c, where m/n are real constants. where both m and n are zero, the vectors are independent. (Also note that if any of the vectors are zero vectors, the set is automatically linearly dependent)

to prove coplanarity of three vectors a, b and c, you need to show that there exists parallel vectors which are penpendicular to a, b and c.
In application, however, it is easier to work with unit vectors. There will be two solutions (one pointing up from a plane, and one pointing down from the plane). Let them be denoted by N, then:
N.a = 0
N.b = 0
|N| = 1
solving that, you can find what N is, and thus find if N is perpendicular to c by another dot product.

though I REALLY doubt VCAA would do something like this, it'll give uni maths students too much of an advantage [it is a one step process using the box product, which is not taught in specialist]