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- Given the plane curve $\vec{r}(t) = \langle t-2, t^2 - 1 \rangle$\\ Sketch the position vector $\vec r (t)$ and the tangent vector $\vec r \ '(t)$ at $t = 1$
- Given $\vec b = \langle 0, 4, 5\rangle$ and $\vec c = \langle -1, 3, -2\rangle$, find $proj_{\vec b}{\vec c}$.
- Find the plane that goes through the points $\left(3, 0, -4\right)$, $\left(-2, -2, 5\right)$, and $\left(-1, 8, -3\right)$.
- Reparametrize the curve $\vec{r}(t) = (4\cos t)\vec{i} + (4\sin t) \vec{j} + 3t\vec{k}$ with respect to the arc length measured from $(4,0,0)$ in the direction of increasing t.
- Given $\vec{a}, \vec{b} \in \mathbb{R}^3$, show that $\vec{a} \times \vec{b}$ is orthogonal to $\vec{a}$ and $\vec{b}$.

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