(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have 2 parametric vector equations (of a line)

r(t) = (2,-4,4) + t(1,-3,4)

s(t) = (1,-1,0) + t(2,-1,1)

how do i find the coordinates for which they intersect each other?

The answers is (1,-1,0)

2. Relevant equations

x=a+λv, for some λ in ℝ (parametric vector form of line)

3. The attempt at a solution

As in high school, with the form y=mx+b i would make the 2 equations equal to each other, solve for x, then substitute back into either equations to find y.

I've tried making the (x,y,z) components equal to each other, solve for 't' and substitute back in but i can't get the answer in the back of the book

parametic equations

for r(t): x = 2+t, y= -4-3t, z= 4+4t

for s(t): x = 1+2t, y= -1-t, z= t

Now i did

2+t = 1+2t

t = 1

substituting back into x=2+t: x = 3

i did this for also y and x components and got (3, 1/2, -4/3)

hmmmm

I have a feeling that this method isnt correct :s

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# Vector geometry - Intersection of lines

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