91Ó°ÊÓ

For the following exercises, make a table of values for each set of parametric equations, graph the equations, and include an orientation; then write the Cartesian equation. $$\left\\{\begin{array}{l}{x(t)=3 t^{2}} \\ {y(t)=2 t-1}\end{array}\right.$$

For the following exercises, make a table of values for each set of parametric equations, graph the equations, and include an orientation; then write the Cartesian equation. $$\left\\{\begin{array}{l}{x(t)=e^{t}} \\ {y(t)=-2 e^{5 t}}\end{array}\right.$$

For the following exercises, make a table of values for each set of parametric equations, graph the equations, and include an orientation; then write the Cartesian equation. $$\left\\{\begin{array}{l}{x(t)=3 \cos t} \\ {y(t)=2 \sin t}\end{array}\right.$$

For the following exercises, determine whether the two vectors, \(u\) and \(v,\) are equal, where \(u\) has an initial point \(P_{1}\) and a terminal point \(P_{2},\) and \(v\) has an initial point \(P_{3}\) and a teminal point \(P_{4}\) . $$P_{1}=(-1,4), P_{2}=(3,1), P_{3}=(5,5) \text { and } P_{4}=(9,2)$$

For the following exercises, determine whether the two vectors, \(u\) and \(v,\) are equal, where \(u\) has an initial point \(P_{1}\) and a terminal point \(P_{2},\) and \(v\) has an initial point \(P_{3}\) and a teminal point \(P_{4}\) . $$P_{1}=(6,11), P_{2}=(-2,8), P_{3}=(0,-1) \text { and } P_{4}=(-8,2)$$

For the following exercises, use the vectors \(u=2 i-j, v=4 i-3 j,\) and \(w=-2 i+5 j\) to evaluate the expression. $$u-v$$

For the following exercises, use the vectors \(u=2 i-j, v=4 i-3 j,\) and \(w=-2 i+5 j\) to evaluate the expression. $$2 v-u+w$$

For the following exercises, find a unit vector in the same direction as the given vector. $$a=8 i-6 j$$

For the following exercises, find a unit vector in the same direction as the given vector. $$\boldsymbol{b}=-3 \boldsymbol{i}-\boldsymbol{j}$$

For the following exercises, find the magnitude and direction of the vector. $$\langle 6,-2\rangle$$