Vector equation of a plane

  • #1

Homework Statement





Write a vector and parametric equation for a plane that:

b) contains (-5,9,-3) and is parallel to [x,y,z] = [1, -2, 7] + s[4, -1, -3] and

[x,y,z] = [7,-2,15] + t[1,6,-8]



The Attempt at a Solution


I'm not sure where to start. Usually, when asking for parallel lines, I find if the direction vectors are scalar multiples of each other, then I find out if s and t have the same value for all x y and z.



I'm confused about planes.
What they had as the answer was the exact same direction vectors s and t, and then the point given as r nought.
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
965
The vector form for a plane is
[tex]\vec{r}= (x_0+ As+ Bt)\vec{i}+ (y_0+ Cs+ Dt)\vec{j}+ (z_0+ Es+ Ft)\vec{k}[/tex]
where [itex](x_0, y_0, z_0)[/itex] is any point in the plane and
[tex]A\vec{i}+ C\vec{j}+ E\vec{k}[/tex]
and
[tex]B\vec{i}+ D\vec{j}+ F\vex{k}[/tex]
are two vectors in the plane.

In your question, you are given all three of those things.
 

Related Threads on Vector equation of a plane

  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
4
Views
916
Replies
1
Views
93
Replies
2
Views
875
Replies
6
Views
4K
  • Last Post
Replies
2
Views
724
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
2K
Top