Find Point of Intersection for Planes in 3D Space

[miglo]

Homework Statement

find the point of intersection of the lines x=2t+1, y=3t+2, z=4t+3 and x=s+2, y=2s+4, z=-4s-1
then find the plane determined by these lines

Homework Equations

The Attempt at a Solution

i have no idea how to find the point of intersection for those two lines
but i figured that I am going to need that in order to find the plane, since ill need a point and the normal vector to find the plane, and i can just find the normal vector by using the cross product on the two vectors that are parallel to the lines
but I am stuck on the very first part, how do i find the intersection?

 

[Dick]

Homework Statement

find the point of intersection of the lines x=2t+1, y=3t+2, z=4t+3 and x=s+2, y=2s+4, z=-4s-1
then find the plane determined by these lines

Homework Equations

The Attempt at a Solution

i have no idea how to find the point of intersection for those two lines
but i figured that I am going to need that in order to find the plane, since ill need a point and the normal vector to find the plane, and i can just find the normal vector by using the cross product on the two vectors that are parallel to the lines
but I am stuck on the very first part, how do i find the intersection?

Since 2t+1=x and s+2=x you can say that 2t+1=s+2. Can you see what to do now?

 

[miglo]

solve for one of the variables?

 

[Dick]

solve for one of the variables?

Sure. You can use y and z to make two more equations. Solve them for t and s. You've got three equations in the two unknowns s and t.