Thread: basic vectors help

1. basic vectors help

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

2. Re: basic vectors help

Originally Posted by disintegration

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 $\displaystyle D=C+(A-B).$

3. 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.

4. Re: basic vectors help

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

5. Re: basic vectors help

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 $\displaystyle \overrightarrow {BA} = \overrightarrow {CD}$.
$\displaystyle A-B$ gives us $\displaystyle \overrightarrow {BA}$ this we get $\displaystyle D$ by $\displaystyle C+(B-A)$.