The Punipuni Vector


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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.)

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foundation of vectors

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

  1. what is a vector??
  2. position vector
  3. addition of position vectors

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 !

  1. relationship between geometry and algebra
  2. 3D figures described by vectors

straight line

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.

  1. scalar multiplication (1)
  2. scalar multiplication (2)
  3. scalar multiplication (3)
  4. orbit of points
  5. line passing through the origin
  6. vector equation

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.

  1. line passing through the origin
  2. how to move the line
  3. each vectors have paticular roll
  4. several vactors that can describe lines
  5. parallel lines
  6. relation between line and two points

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.

  1. line passing through the origin
  2. line which pass through fixed one point and has fixed direction vector
  3. line which pass thorugh fixed one point and is parallel to another line
  4. line passing through fixed two different points


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.

  1. review of line
  2. slided line
  3. adding extendable vector
  4. animate all vectors simultaneously
  5. vector expressing the plane

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. "

  1. normal vector and plane's direction
  2. normal vector, point, plane
  3. vector which describe paticular point
  4. vector equation of plane
  5. plane passing through the origin
  6. orbit of points
  7. inner product is zero
  8. plane which does NOT pass through the origin
  9. normal vector is...
  10. formula of plane

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)

  1. distance?
  2. normal vector, points, and plane
  3. vector which describes distance
  4. formula of the distance between the origin and fixed point

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.

  1. line passing through three fixed points
  2. plane which has a normal vector and pass through a fixed point


afterwords form translator

we hope you have enjoyed Punipuni Vector!

- 2011.04.27 punipuni translator