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Intersection of two vectorvalued functions 
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#1
May1610, 08:28 PM

P: 7

1. The problem statement, all variables and given/known data
Prove that r1 and r2 intersect at (1,1,3). Let r1 and r2 be defined as: r1(t)=t^2i+tj+3t^3k r2(t)=(t−1)i+(1/4)t^2j+(5−t)k 2. Relevant equations Intersection is derived from r1=r2. 3. The attempt at a solution I only formally get to this point and then start messing up. It gets messy and I know i'm not doing the right thing. r1=r2 > t^2i+tj+3t^3k = (t−1)i+(1/4)t^2j+(5−t)k 


#2
May1610, 08:44 PM

HW Helper
P: 3,307

it may help to write the curves with different parameterisation variables
r1(s)=s^2i+sj+st^3k r2(t)=(t−1)i+(1/4)t^2j+(5−t)k then solve for correspdoning intersection point in terms of s & t 


#3
May1610, 08:56 PM

Mentor
P: 21,215

In this problem, all you need to do is to show that (1, 1, 3) is a point on both curves. In the first function, what value of t gives this point? In the second function what value of s gives the same point? 


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