- #1

Alettix

- 177

- 11

## Homework Statement

As part of a longer problem:

"Find necessary and sufficient conditions for the point with positionvector

**r**to lie inside, or on, the tetrahedron formed by the vertices

**0, a, b**and

**c**."

## Homework Equations

I am not sure... vector addtion?

## The Attempt at a Solution

I don't really know how to attack this problem. I was thinking that all points inside the tetrahedron must be able to be decomposed into vectors along

**a,b,c**provided that these are not coplanar (which they cannot be if they form a tetrahedron):

**r**= α

**a**+ β

**b**+ γ

**c**

However, some restriction must be placed on the coefficients. I think 0≤α+β+γ≤1 is a condition, but it is not sufficient (imagine for instance |

**a**| >> |

**b**| and let α=-1.5 and β=2, clearly

**r**can get outside the tetrahedron).

I feel very lost regarding this problem and appreciate any help and guidance. :)