Point of intersection between plane and line?

Click For Summary
SUMMARY

The intersection point between the plane defined by the equation x - 2y + 3z = 11 and the line represented by the parametric equation <1,0,-2> + t<3,-1,2> is confirmed to be (59/11, -16/11, 10/11). Participants in the discussion emphasized the importance of verifying this solution by substituting the coordinates into the plane's equation and ensuring the point lies on the line. Mark44 specifically encouraged a thorough check to eliminate any doubts regarding the correctness of the solution.

PREREQUISITES
  • Understanding of linear algebra concepts, specifically planes and lines in three-dimensional space.
  • Familiarity with parametric equations and how to manipulate them.
  • Knowledge of substitution methods for verifying solutions in equations.
  • Basic skills in solving systems of equations.
NEXT STEPS
  • Learn how to derive intersection points between planes and lines in three-dimensional geometry.
  • Study the method of substitution for verifying solutions in linear equations.
  • Explore the use of vector notation in representing lines and planes.
  • Investigate the implications of intersection points in geometric applications.
USEFUL FOR

Students and professionals in mathematics, particularly those studying geometry and linear algebra, as well as anyone involved in fields requiring spatial analysis and problem-solving in three dimensions.

whig4life
Messages
14
Reaction score
0
intersection between x-2y+3z=11 and <1,0,-2> + t<3,-1,2>

my attempted solution

(59/11, -16/11, 10/11)
 
Physics news on Phys.org
whig4life said:
intersection between x-2y+3z=11 and <1,0,-2> + t<3,-1,2>

my attempted solution

(59/11, -16/11, 10/11)
You know how to check that this really is a solution, right?
 
It fits according to what I know, but I feel like something is wrong.
 
whig4life said:
It fits according to what I know, but I feel like something is wrong.

Mark44 is suggesting you actually check it. Put those numbers into the equation for the plane. Does it work? Check again that it is on the line. Then you won't have to feel like something is wrong.
 
Show us how you did your check. If there's something wrong, I'm sure we'll spot it.
 

Similar threads

Finding the point on the line of intersection between planes
  • · Replies 5 ·
Replies
5
Views
2K
Distance between two parallel lines
  • · Replies 2 ·
Replies
2
Views
2K
Proof that the images of parallel lines under an isometry are parallel
  • · Replies 4 ·
Replies
4
Views
1K
Lattice point problem from Stewart's Calculus
  • · Replies 21 ·
Replies
21
Views
3K
Find the volume bounded by hyperboloid and plane z = ± d
  • · Replies 14 ·
Replies
14
Views
2K
Intersection of Lines: Solving for m and n to Determine Concurrent Lines
  • · Replies 5 ·
Replies
5
Views
2K
Vector parametric equation of line
  • · Replies 9 ·
Replies
9
Views
1K
Why Are There No Solutions to This Vector Equation Problem?
  • · Replies 5 ·
Replies
5
Views
2K
How do I find a plane that contains two given lines?
  • · Replies 3 ·
Replies
3
Views
2K
Intersection of line through a plane
  • · Replies 2 ·
Replies
2
Views
1K