Thread: Vector difficulties

I am having some difficulties doing some basic vector questions on an assignment.

a line L1 passes through (1,-1,4) and is parallel to vector (1,-1,1). Another line L2 passes through (2,4,7) and (4,5,10). obtain teh vector lines equations for L1 & L2. Do the two lines intersect, if so at what point?

I think I have correctly worked out the line equations as:

for L1: r = (1,-1,4)+λ(1,-1,1) Edit: thanks to plato
for L2: r = (2,4,7)+λ(2,1,3)

But I am unsure how to work out if they intersect, and if so where?

Do i need to calculate their cartisan equations, and if so how do I then determine the intersect point.

Thanks for your time

Originally Posted by nickskely

[I]a line L1 passes through (1,-1,4) and is parallel to vector (1,-1,1). Another line L2 passes through (2,4,7) and (4,5,10). obtain teh vector lines equations for L1 & L2. Do the two lines intersect, if so at what point?
for L2: r = (2,4,7)+[/B]λ(2,1,3)

The first line is

Thanks for that Plato, but I am still not sure how to proceed to work out if and where the lines intersect?

Originally Posted by nickskely

I am still not sure how to proceed to work out if and where the lines intersect?

Write each line in parametric form using a different parameter:


Now pick two of the coordinates and solve the equations.
(Be sure you check the solution in the coordinate that was not used.)

Thanks, but I am still unclear...

are you saying I need to find the value of λ and μ that will make X (if chosen) equal for both coordiantes?

thanks in advance

Solve the system: .

But make sure that it also works in .

ok, I see now

So I got:

λ = -3
μ = -2

and it also satisfies Z

So is -3,-2 my intersection point?

and what would the Z value be?
-3,-2,0?

thanks again