# Math Help - Vector-Valued functions

1. ## Vector-Valued functions

Hello everyone.

I need to solve this math problem and it has been giving me lots of trouble.

Find all values of t such that r'(t) is parallel to the xy-plane.

r(t)=<sqrt(t+1), cos(t), t^4-8t^2>

Thanks!

2. Originally Posted by palmaas
Hello everyone.

I need to solve this math problem and it has been giving me lots of trouble.

Find all values of t such that r'(t) is parallel to the xy-plane.

r(t)=<sqrt(t+1), cos(t), t^4-8t^2>

Thanks!

The normal vector to the xy-plane is $\hat{k}$.

Whe the normal of the plane is perpenduclar to $r'(t)$
the vector will be parallel to the plane.
So when $\hat{r}'(t)\cdot \hat{k}=0 \iff 4t^3-16t=0$.