Are the given lines in R^3 concurrent or parallel?

[rickster1]

Homework Statement

Ok I have a bunch of questions, please bare with me and i'd appreciate it VERY much if you could help me with these!

1. Assume that you are given the equations of three planes. Without solving the system, describe a "test" with rationale, that you could use to determine whether or not the planes intersect at a single point.

2. Given the equations of three lines in R^3

L1 = (1,4,1) + t(3,3,-2)
L2 = (-3,-5,8) + r(5,0,1)
L3 = (3,-5,8) + s(-5,0,-1)

a) Can all three lines be concurrent (i.e interesect at one point)? Algebraic solution not required

b) Determine the point of intersection of L1 and L2

c) Use information of part a) to help in determining the distance between L3 and L2


End questions.


I'd appreciate it a lot if someone can help me... :(

Homework Equations

I'm not sure, I got these questions on a whim and my textbook doesn't offer much help other than simple formulas.

The Attempt at a Solution

I'm really unsure how to approach these questions.. I got them on a whim and I haven't faced this unit of calculus before..

 

[jegues]

Can you make more of an attempt at the questions? It's better you show us what you think instead of us just telling you the answers.

I'll get you started.

For 2a) a good place to start would be to determine whether any of the lines are parallel or not. After all, if they are parallel to one another, surely they won't intersect!

HINT: Look at the direction vectors of the each line.