Lines in 3D Space (Parametric, Vector, and Cartesian Forms)

form

parametric

vector

Cartesian

show line

You can vary the line: the boxes

in the result are pull-down menus!

t

0

show grid

grid

xy

yz

zx

move grid

0



x

y

z

 = 

a

c

e

 + 

b

d

f

t = 

1

2

1

 + 

1

-1

0

 (0) = 

1

2

1



This Demonstration shows the equation of a line in 3D in three different forms: parametric, vector, and Cartesian. You can vary the line—the boxes in the result are pull-down menus. You can also choose to show a grid, which you can move parallel to the

x

-

y

,

y

-

z

, or

z

-

x

plane. As you do this, the color of the line will change where it intersects the grid. By changing the value of the parameter

t

, you can locate a particular point on the line.