Vector Equation for Plan Containing Two Lines

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Homework Help Overview

The problem involves determining a vector equation for a plane that contains two given lines, L1 and L2, represented in vector form. The lines are defined by specific points and direction vectors.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the possibility of finding a point of intersection and consider whether a parameter is missing from the definition of L2. There are suggestions to find multiple points on the lines to define the plane.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to defining the plane. Some guidance has been offered regarding the need for parameters and the use of points from the lines to establish the plane's equation.

Contextual Notes

There is a noted confusion regarding the parameters in the representation of L2, which may affect the overall approach to the problem. Participants are also considering the implications of finding a point of intersection.

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Homework Statement



Determine a vector equation for the plan that contains the following two lines:
L1=(4,-3,5)+t(2,0,-3) and L2=(4,-3,5)+(5,1,-1)


The Attempt at a Solution



I tried finding the point of intersection, but that was wrong. I am completely lost.
 
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menal said:

Homework Statement



Determine a vector equation for the plan that contains the following two lines:
L1=(4,-3,5)+t(2,0,-3) and L2=(4,-3,5)+(5,1,-1)


The Attempt at a Solution



I tried finding the point of intersection, but that was wrong. I'm completely lost.

Are you missing a parameter from L2 ?

Sould it be something like L2=(4,-3,5)+s(5,1,-1) ?
 
point of intersection is not a bad start - show your work

however why not find 3 points on the lines (2 on one and one on the other), this should be enough to define the equation of your plane

how do you plan to define the plane?
 
yes! sorry! din realize that i was issing the "s"
 
The point of intersection looks obvious.
 
(4,-3,5) right?
 
Right.
 
alright so the direction would be:
a=(2,0,-3)
b=(5,1,-1)

and a point is: (4,-3,5)
so the final equation would be:
r=(4,-3,5)+s(2,0,-3)+t(5,1,-1)
is that correct?
 
Looks good to me.
 

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