Math Help - Vector: Coordinates and Parallel Lines

1. Vector: Coordinates and Parallel Lines

This is part of a carried on question. I don't know how to do the posted part.Help would be appreciated.

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Q:

Referred to an origin $O$, the point $A$, $B$, $C$ have coordinates $(3, 2, 0)$, $(1, 0, 1)$, $(2, 2, 2)$ respectively.
(i) Point $D$ $(4, 4, 1)$ lies on the plane. Show that $AB$ and $DC$ are parallel.
(ii) Find the coordinates of the point where the line $AC$ and $BD$ meet.

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2. Originally Posted by Air
This is part of a carried on question. I don't know how to do the posted part.Help would be appreciated.

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Q:

Referred to an origin $O$, the point $A$, $B$, $C$ have coordinates $(3, 2, 0)$, $(1, 0, 1)$, $(2, 2, 2)$ respectively.
(i) Point $D$ $(4, 4, 1)$ lies on the plane. Show that $AB$ and $DC$ are parallel.
find AC and DC and show that they are scalar multiples of each other

3. Originally Posted by Air
(ii) Find the coordinates of the point where the line $AC$ and $BD$ meet.

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write AC and BD as (3-dimensional) lines. then equate corresponding components. you will get a set of simultaneous equations to solve. the solution will give you the point

4. Originally Posted by Air
Q:

Referred to an origin $O$, the point $A$, $B$, $C$ have coordinates $(3, 2, 0)$, $(1, 0, 1)$, $(2, 2, 2)$ respectively.
(i) Point $D$ $(4, 4, 1)$ lies on the plane. Show that $AB$ and $DC$ are parallel.
(ii) Find the coordinates of the point where the line $AC$ and $BD$ meet.
This question is nearly a trick question:

Since

$|\overrightarrow{AB}| = |\overrightarrow{CD}| = 3$

you are dealing with a parallelogram. Therefore the point of intersection is the midpoint of AD or BC: M(2.5, 2, 1)