Section 13.2 – Derivatives and Integrals of Vector Functions
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Find a vector equation for the tangent line to the curve \(\mathbf{r}(t) = \left< 4\sqrt{t}, t^2-10, \dfrac{4}{t} \right>\) at \((8,6,1).\)
\(\mathbf{r}(t) = \left< 8+t, 6+8t, 1-\dfrac{1}{4}t \right>\)
2. The curves \(\mathbf{r}_1(s) = \left< s, s^2, 2e^{3s-3} \right>\) and \(\mathbf{r}_2(t) = \langle \cos(t), t^3+t+1, 3t+2 \rangle\) intersect at \((1,1,2)\). Find their angle of intersection.
\(\theta = \cos^{-1}\left(\dfrac{20}{\sqrt{410}}\right)\)