Teaching C4 Vectors with Autograph
Status box and Results box are useful
View > Status box
View > Results box
The Object menu can be used as an alternative to right-click.
2D Vectors
Creates a new 2D page
Equal Aspect is useful
The basics

Definition (component vs magnitude & direction form)
Places a point on the screen
or
Allows you to enter coordinates
(Remember to return to Cursor mode:
)
Right-click on the point and select Vector…
Vectors can be added in component or magnitude and direction form

Equal vectors
Vectors can be moved by dragging the start-point

Position vectors
Dragging the start-point to the origin is equivalent to a position vector

Multiplying by a scalar
Select the start-point and the vector
Right-click and select Multiply Vector

Negative vectors
Select the start-point and the vector
Right-click and select Negative Vector

Adding
Create two vectors (better with different start-points)
Select one point and two vectors
Right-click and select Add Vectors
The vectors can be moved to show a closed triangle

Subtracting
As with adding vectors
A negative vector can be used to show a closed triangle

Unit vectors
Select the start-point and the vector
Right-click and select Unit Vector
The unit vector is shown in the results bar
Teaching C4 Vectors with Autograph
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Co-ordinate Geometry

Vector joining 2 points
Place two points on the screen
Select both points (select the 1st then hold down shift-select the 2nd )
Right-click and select Create Vector
The “Join Vector” is shown in the status bar at the bottom

Vector equation of a line
Select
and enter a vector equation of a line
or
Select a point and a vector, right-click and select Line from Vector

The concept of the vector equation of a line
Create a line defined by a vector equation
 x   4 
 3
 
 y   1 
 2
e.g.    

Create points at (0, 0), (-4, -1) and (-4 + 3a, -1 + 2a)
NB a is representing 
(as an alternative you can use from the onscreen keyboard).
Create vectors joining each pair of points
Vary a using the constant controller:
All three Join Vectors can be investigated as a changes

Cartesian vs. vector form of a line
Vector and Cartesian forms can be entered on the same axes

Intersection of 2 lines
Select 2 lines, right-click and select Solve intersections
Angles and Scalar Product

Scalar product
Select 2 vectors, right-click and select Scalar product

Angle between two vectors
Select 2 vectors, right-click and select Angle between vectors

Perpendicular vectors
Select a point and a vector, right-click and select Perpendicular vector
Teaching C4 Vectors with Autograph
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3D Vectors
Creates a new 3D page
Vectors and points can be added in the same way as on 2D pages
Entering co-ordinates is often easier than adding points
Vectors and lines in 3D

Points in 3D
Add a point, right-click and select Draw Coordinate box
Axes > Edit Axes > Option > Always Outside switched off can be useful

Angle between 2 vectors
Select 2 vectors, right-click and select Scalar product
Using 2 vectors with the same start-point and placing a plane on the
screen can help to visualise this

Equation of a line
Select
and enter a vector equation of a line
or
Select a point and a vector, right-click and select Line from Vector

Intersection
Select 2 lines, right-click and select Intersections

Angle between 2 lines
Select 2 lines, right-click and select Angle between lines
Planes

Vector form (3 points)
Select
and enter a vector equation of a plane
or
Select 3 points, right-click and select Plane
or
Select 2 vectors with the same start-point and the start-point, right-click
and select Plane

Cartesian form
Select
or press Enter and enter a Cartesian equation of a plane

Perpendicular to a plane
Select a plane and a point on it, right-click and select Normal line
or Normal Unit Vector
or
Select a vector and a point, right-click and select Plane from vector

Intersection of a line and a plane
Select a line and a plane, right-click and select Intersection

Distance of a point from a plane
Select a point and a plane, right-click and select Closest distance
Teaching C4 Vectors with Autograph
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Advanced 3D Vector Geometry with Autograph
Creates a new 3D page
and
zoom in or out on the axes.
changes the camera angle.
Ctrl +
Shift +
zooms in or out of the box (without changing the axes).
moves the box (without changing the axes).
Status box and Results box are useful
View > Status box
View > Results box
The Object menu can be used as an alternative to right-clicking.
Adding points and vectors
See: C4 Vectors with Autograph
Entering co-ordinates is often easier than adding points.
3D Vectors – Vector product, lines and planes
Vector (Cross) Product
Select 2 vectors and a point, right-click and select Cross product
It should then be possible to show that the Scalar Product of this vector
with each of the original ones is 0.
You can also show the related Cartesian equation of the plane containing 2
vectors has coefficients equal to the components of normal vector.
Intersection of 2 planes
Select 2 planes, right-click and select Intersection line
Angle between 2 planes
Create a point not on either plane.
Select the point and one of the planes, right-click and select Normal Line.
Select the point and the other plane, right-click and select Normal Line.
Select both lines, right-click and select Angle between lines.
Intersection of 2 lines
Select 2 lines, right-click and select Intersection.
The co-ordinates of the point or “No intersection” is displayed.
Distance between a point and a line/plane
Select a point and a line/plane, right-click and select Closest Point.
Shortest distance between two lines
Select 2 lines, right-click and select Shortest Distance.
Teaching C4 Vectors with Autograph
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