Help on Vector proof? :)

[poohead]

 This comes out of the Heinemann book:
Prove that the medians intersect at a common point two-thirds of the distance from
each vertex. (Note: The median is the line joining a vertex to the mid-point of the
side opposite.)
Help please??

[kyzoo]

The vertex of what?

[poohead]

my bad
Of a triangle

The sides of triangle ABC are represented by the vectors AB=a, BC=b, CA=c
such that a+b=-c
Prove that the medians intersect at a common point two-thirds of the distance from
each vertex. (Note: The median is the line joining a vertex to the mid-point of the
side opposite.)

[brightsky]

Probably approach it from a different angle?

Let M, N, O be the points on the median two-thirds of the distance vertices A, B, C respectively.

Let D, E, F be the midpoints of AC, CB and AB respectively.

Prove .

[Martoman]

This involves a tiny bit of work.

Key observations to make is that the median bisects the line it meets in half.

Also that you can find multiple, equivalent, routes to the same vector and use this to derive the desired ratios.

Link to my working is : http://img697.imageshack.us/i/proofi.jpg/

Enjoy

[poohead]

ohhh i see
thanks (Y)

[rainbows.]

This a vector related questions, well questions.. and i just wanna get help on since im totally blanking out atm

What is the unit vector perpendicular to -3i + 3j?
&
If u = -4i +aj, v =2ai -aj and u is perpendicular to v, then what is a?

THANK YOU

[rainbows.]

AND AND is the vector u = 2ti + (6-8t)j a straight line? or is it a parabola? Or any other sort of graph.. imsure its a straight line right? 

[m@tty]

If and and is perpendicular to then what is a?

.





.

is a trivial solution so I'm guessing is what you are looking for.

[m@tty]

AND AND is the vector u = 2ti + (6-8t)j a straight line? or is it a parabola? Or any other sort of graph.. imsure its a straight line right?  

Parametrically:

and

Now you need to manipulate the 't' parts so you can equate two expressions so you are left with only x and y.



Now equate this expression with the one for y.

.

So yes, a straight line.

[m@tty]

This a vector related questions, well questions.. and i just wanna get help on since im totally blanking out atm

What is the unit vector perpendicular to -3i + 3j?

I have forgotten how we are 'meant' to do this...

But,

The gradient of the vector is -1, therefore the gradient of the normal will be 1.

And the unit vector with gradient 1 is .