Lines and Planes in 3-D
Linear Equations:
In 2-D:
Ax
+
By
=
C
What is the graph?
D
What is the graph?
Review Parametric Equations
General 2-D:
Example:
x
=
f
(
t
)
y
=
g
(
t
)
x
=
t
2
y
=
4
t
2
What about 3-D?
Lines in 3-D
Given:
P
1
(
x
1
,
y
1
,
z
1
)
is a specific point on the line
v
=
a
,
b
,
c
is a vector parallel to the line
Find:
Parametric Equations to describe all of the points
P
(
x
,
y
,
z
)
on the line
Parametric Equations for the line that passes through the point P(x1,y1,z1)and is parallel to the vector v =a,b,cx=x1+aty=y1+btz=z1+ct___________________________________________________ Find parametric equations for the line that passes through P1(4,−1,3)and is parallel to v=2,1,−4Does the point Q(6,0,−1)lie on the line? Does the point R(1,2,−3)lie on the line? Is the line parallel to the vector w=−4,−2,8Is the line parallel to the vector w=6,3,−4
:
.
?
?
