# Need help with this vector problem -- Thank you

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1. May 14, 2017

### uchuu-man chi

1. The problem statement, all variables and given/known data
Let L1 be the tangent line to r(t) at the point t = a and let L2 be the tangent line where t = b. Find the equation of the lines L1. Find the equation of the lines L1 and L2 and find the points of intersection.

r(t) = <f(t), g(t), h(t)>

*bolded letters are vectors
2. Relevant equations

3. The attempt at a solution
I just wanted to tell you guys my thought process and would you correct me wherever I am wrong. The question has more to it, but the computation would be menial. I'm just having trouble with what vectors to use and all that stuff.

Steps I would take:
-r(a) would give me a point on L1 and r(b) would give me a point on L2.
-find T(t)
-find T(a) and T(b)
-for L1, the equation of line would be (f(a), g(a), h(a)) + T(a)t
-same step for L2 as L1
-find if there is an intersection by setting the parameters of x,y, and z of the lines equal

Am I using the correct vector, T(t), for the second step?

Last edited: May 14, 2017
2. May 14, 2017

### BvU

Did you forget to tell us what T is ?
And: do you always expect to find an intersection ?

3. May 14, 2017

### uchuu-man chi

OOps sorry

the T(t) would be $$\frac {\vec r '(t)} {||\vec r '(t)||}$$
And no I wouldn't expect to always find an intersection. The lines could be parallel or skew

Last edited: May 14, 2017
4. May 15, 2017

### BvU

In that case: so far, so good !