# Thread: Deduce Triangle Equality! [Vectors]

1. ## Deduce Triangle Equality! [Vectors]

Alright people im struggling with this vector question;

Deduce the triangle inequality,
||a-c|| <= ||a-b|| + ||b-c||

Ive been stuck on this question for ages now, and ive tried various attempts to solving it.

Can any one help me out? Cheers
David.

2. Did you think about using vectors ?

3. Originally Posted by Bacterius
Did you think about using vectors ?
You mean give an example and show it holds?
I dont think thats valid as you have to deduce it?

4. No, I meant using vector properties (they go quite well with triangles) and look if you can't work out your equality from this. By the way, is your triangle scalene or is it some particular type of triangle ? And what do you mean by ||a-c|| ? Does it mean the length of the vector $\displaystyle \vec{AC}$, which is $\displaystyle ||\vec{AC}||$ ?

5. Originally Posted by Bacterius
No, I meant using vector properties (they go quite well with triangles) and look if you can't work out your equality from this. By the way, is your triangle scalene or is it some particular type of triangle ? And what do you mean by ||a-c|| ? Does it mean the length of the vector $\displaystyle \vec{AC}$, which is $\displaystyle ||\vec{AC}||$ ?
Yeah i tryed using vector properties and yeah || a || means the length of the vector a e.g. (a1^2 + a2^2 + ... + an^2)^1/2

I still couldent work it out, using properties like;

|| a - b ||^2 = ||a||^2 ||b||^2 -2cos x.

6. Originally Posted by simpleas123
Yeah i tryed using vector properties and yeah || a || means the length of the vector a e.g. (a1^2 + a2^2 + ... + an^2)^1/2

I still couldent work it out, using properties like;

|| a - b ||^2 = ||a||^2 ||b||^2 -2cos x.
||a-c|| <= ||a-b|| + ||b-c||

Does it mean :

$\displaystyle ||\vec{AC}|| <= ||\vec{AB}|| + ||\vec{BC}||$ ?

One really needs to know what you mean to be able to help you.

7. Originally Posted by Bacterius
||a-c|| <= ||a-b|| + ||b-c||

Does it mean :

$\displaystyle ||\vec{AC}|| <= ||\vec{AB}|| + ||\vec{BC}||$ ?

One really needs to know what you mean to be able to help you.
Yes it does, sorry for the fusion.

I know that $\displaystyle ||\vec{AC}|| = ||\vec{AB}|| + ||\vec{BC}||$
If and only if the dot product of two of the vectors = 0.