Find the vectors whose lengths and directions are given. Try to do the calculations without writing.

Length $\quad \quad$Direction

$(c)$. $\displaystyle \frac{1}{2} \quad \quad \quad \frac{3}{5} \mathbf{j}+\frac{4}{5} \mathrm{k}$

Find the vectors whose lengths and directions are given. Try to do the calculations without writing.

Length $\quad \quad$Direction

(a). $2 \quad \quad \quad\quad \mathrm{i}$

Find the vectors whose lengths and directions are given. Try to do the calculations without writing.

Length $\quad \quad$Direction

(b). $\sqrt{3} \quad \quad -\mathbf{k}$

Find the distance from the point $(3,-4,2)$ to the

(b). $y z$-plane

Let $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ be vectors. and which do not? Give reasons for your answers.

(b). $\mathbf{u} \times(\mathbf{v} \cdot \mathbf{w})$

Find the distance from the point $(3,-4,2)$ to the

(b). $y z$-plane

Find the general solution of the given differential equation, and use it to determine how solutions behave as $t \rightarrow \infty$.

$$y^{\prime}+y=5 \sin (2 t)$$

Find the distance from the point (3, -4, 2) to the a. xy-plane b. yz-plane c. xz-plane.

Find the distance from the point (3, -4, 2) to the a. xy-plane b. yz-plane c. xz-plane.

Find the general solution of the given differential equation, and use it to determine how solutions behave as $t \rightarrow \infty$.

$$t y^{\prime}-y=t^2 e^{-2 t}, \quad t>0$$

Find the general solution of the given differential equation, and use it to determine how solutions behave as $t \rightarrow \infty$.

$$y^{\prime}+3 y=t+e^{-2 t}$$

Find the general solution of the given differential equation, and use it to determine how solutions behave as $t \rightarrow \infty$.

$$y^{\prime}-4 y=t^2 e^{4 t}$$

Find the general solution of the given differential equation, and use it to determine how solutions behave as $t \rightarrow \infty$.

$$3 y^{\prime}+4 y=t^2$$

Find the general solution of the given differential equation, and use it to determine how solutions behave as $t \rightarrow \infty$.

$$y^{\prime}+4 y=t+e^{-2 t}$$