# basic vectors help

• Jun 7th 2012, 12:55 PM
disintegration
basic vectors help
Attachment 24043

Hi there,

I'm stuck on the above question (part b). The part i'm actually stuck on is adding vector components (I think this is what it's called)

ABCD is a rectangle. I have the coordinates of A (4, -2, 3), B (2, 0, -1) and C (5.5, 5.5, 0).

To find D i'm told by the markscheme that OD = OA + BC. What does this actually mean?

I don't have anything like this in the book i've been studying from so i've no idea how to complete the question.

Thank you for any help
• Jun 7th 2012, 01:37 PM
Plato
Re: basic vectors help
Quote:

Originally Posted by disintegration
Attachment 24043

ABCD is a rectangle. I have the coordinates of A (4, -2, 3), B (2, 0, -1) and C (5.5, 5.5, 0).

To find D i'm told by the markscheme that OD = OA + BC. What does this actually mean?

You can find $D=C+(A-B).$
• Jun 7th 2012, 01:44 PM
HallsofIvy
Re: basic vectors help
What I would do is this: find the equation of the plane, containing B, perpendicular to the vector AB. Determine where the line l crosses that plane. That will be the point "C". After that, it should be easy.
• Jun 8th 2012, 05:12 AM
disintegration
Re: basic vectors help
Quote:

Originally Posted by Plato
You can find $D=C+(A-B).$

This is the thing, I don't understand these basics or why that will give the coordinates of D. Is there anywhere I can learn this stuff?
• Jun 8th 2012, 05:24 AM
Plato
Re: basic vectors help
Quote:

Originally Posted by disintegration
This is the thing, I don't understand these basics or why that will give the coordinates of D. Is there anywhere I can learn this stuff?

It is basic geometry. Opposite sides of a rectangle are parallel and have the same length.
In case of vectors this means $\overrightarrow {BA} = \overrightarrow {CD}$.
$A-B$ gives us $\overrightarrow {BA}$ this we get $D$ by $C+(B-A)$.