# Thread: The smallest distance between two vectors?

1. ## Re: The smallest distance between two vectors?

Actually, I understand the perpendicularness, but wouldn't using that equation find the smallest distance between the velocity vector and position of the plane at any time? Not the plane and station?

2. ## Re: The smallest distance between two vectors?

Therefore you are in the state of Victoria Australia and you compete for a Victorian Certificate of Education. (V.C.E) .
GOOD LUCK FOR THIS.

MINOAS

3. ## Re: The smallest distance between two vectors?

Yes, yes I am :P Thanks man!

4. ## Re: The smallest distance between two vectors?

Originally Posted by iamapineapple
Hahaha, I'm in Australia so I'm a 'VCE' student. Last year of school, highest level of maths available but the difficulty or structure should be similar to international courses I assume.

This may be a bit too much.
If $\displaystyle \ell_1=P+tD~\&~\ell_2=Q+tE$ are skew lines (neither are parallel nor do they intersect) then the distance between them is:
$\displaystyle \frac{{\left| {\overrightarrow {PQ} \cdot \left( {D \times E} \right)} \right|}}{{\left\| {D \times E} \right\|}}$

5. ## Re: The smallest distance between two vectors?

Is this an actual formula? ^

6. ## Re: The smallest distance between two vectors?

Originally Posted by iamapineapple
Is this an actual formula? ^
Indeed it is. But I don't know how advanced you are.
To use it, you must understand vector products as a vector which is perpendicular to both vectors.

7. ## Re: The smallest distance between two vectors?

I've covered the basics of vectors but we'll go into more detail when we do vector calculus.

I have a new question if anyone could help me?

Let g: R \ {-13/4 } --> R be another function with f[g(x)] = 3 / (4x + 13). Find the rule of g(x). How should I do this!?!

8. ## Re: The smallest distance between two vectors?

I know that the range of g is a subset of the domain of f, so the function exists, but where to go now?

9. ## Re: The smallest distance between two vectors?

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