Math(Calculus)

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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 soo much if someone can help me... :(

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