• Support PF! Buy your school textbooks, materials and every day products Here!

Intersection between 2 planes

  • #1

Homework Statement



Find the vector equation for the line of intersection of the planes 4x+3y−3z=−5 and 4x+z=5

r = < _, _, 0> + t<3, _, _>

Fill in the blanks for the vector equation.

Homework Equations





The Attempt at a Solution



I used the method of elimination of linear systems.

4x + 3y - 3z = -5 (1)
4x +0y +z = 5 (2)

Subtract equation (1) from equation (2)

(1) - (2)

3y - 4z = -10

Isolate y:

y = 4z/3 -10/3

Next I isolate x from equation (2)

x = -z/4 + 5/4


Let z = t as parameter

Parametric equation:

x(t) = -t/4 + 5/4
y(t) = 4z/3 - 10/3
z(t) = t

From this I know that the point on the line of intersection is (5/4, -10/3, 0)

However for the vector of the line of intersection, I keep on getting the x value as -1/4 and the answer is 3.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
179
##z(t) = t## isn't going to work. Try using ##z(t) = ct## where ##c## is some constant chosen to give you the 3 you need in ##t\langle 3,?,?\rangle##.
 
  • #3
pasmith
Homework Helper
1,738
410
The line of intersection between two planes obviously lies in both planes, and is therefore perpendicular to the normal of each plane. Thus the direction of the line is given by
[tex]
\begin{pmatrix} 4 \\ 3 \\ -3 \end{pmatrix} \times
\begin{pmatrix} 4 \\ 0 \\ 1 \end{pmatrix} =
\begin{pmatrix} 3 \\ ? \\ ? \end{pmatrix}
[/tex]
 

Related Threads on Intersection between 2 planes

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
8
Views
2K
Replies
2
Views
7K
  • Last Post
Replies
8
Views
2K
Replies
4
Views
775
Replies
6
Views
1K
Replies
9
Views
5K
Replies
1
Views
2K
Replies
7
Views
766
Replies
4
Views
8K
Top