*This system can only work on Windows OS with
Opera.*

If you do not use one of them, this system does not work correctly.

So, please check your browser first.
Moreover, becase of this system is partially built by Cabri3D,
*install plug-in of Cabri3D on your PC*.

...Check it? Okay, now welcome to *"Punipuni Vector"*.

This system is for students who can not imagine vectors in three-dimensional (3D).
Supproting them to understand liner algebra is the main porposes of this system.

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*◆Caution !*

We use unique exressions in Punipuni Vector.

For instance vector x is written as "x↑". You know it is not general.

(More details are here about unique expressions.
See also rule of the object's colors in Punipuni Vector.)

We recomend you to use this system by Full screen ( press *F11* key )

position vector

First of all, we need to get an idea of *"position vector"* which acts an important role to describe 3D figures!

3D figures discribed by vectors

This topic is for someone thought *"now, I know what position vector is, but hey, why can they describe 3D figures?"*

Don't worry, we will show it step by step !

line passing through the origin

This is a first step of vector algebra about 3D figures!

First, let's learn about *relationship between vectors and 3D figures* at "line passing through the origin" above.

general form of line's vector equation

By using the idea of "line passing throght the origin"', we will learn how to describe "line which does NOT pass through the origin" next.

Let's specify the difference between extendable vectors and unextendable vectors, here.

basic problems about lines

In this topics, we introduce you how to derive the line's vector equation in the problems.

Let's think how to use vector knowledge for the problem's situations.

plane discribed by vector equation

We use same idea to describe plane by vectors.

plane built by mount of line

In this topic, we will express the plane by the line.
If you can imagine how the plane's vector equation functions at contents above, you can skip this topics.

plane described by inner product

In this topic we will describe plane with inner product.

"Inner product", maybe it sounds like difficult.
But it ok, there is no complicated formulas. We only use its propaty *"inner product becomes 0 in the situation which two vectors are parpenticular to each other. "*

distance between point and plane

We will derive the distance between a plane and a point with formula of plane (that described by inner product)

basic problems about the plane

In this topics, we introduce you how to derive the plane's vector equation in the problems.

Let's think how to use vector knowledge for the problem's situations.

we hope you have enjoyed Punipuni Vector!

- 2011.04.27 punipuni translator