Exam 8: Polar Coordinates; Vectors

Match the graph to one of the polar equations. - A) $r = - 2 \cos \theta$ B) $r \sin \theta = - 1$ C) $r = - 2 \sin \theta$ D) $r = - 1$

Find the requested vector. -v = -4i - 5j + k, w = -5i + 3j - k Find a vector orthogonal to both v and w.

Find the indicated cross product. -v = 4i + 2j + 5k, w = -5i + 2j + 4k Find w × v.

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - $\theta = \frac { \pi } { 3 }$ A) $y=\sqrt{3} x$ ; line through the pole making an angle of $\frac{\pi}{3}$ with the polar axis B) $y=-\frac{\sqrt{3}}{3} x$ ; line through the pole making an angle of $\frac{\pi}{3}$ with the polar axis C) $y=-\frac{\pi}{3}$ ; horizontal line $\frac{\pi}{3}$ units below the pole D) $\left(x-\frac{\pi}{3}\right)^{2}+y^{2}=\frac{\pi^{2}}{9} ;$ circle, radius $\frac{\pi}{3}$ center at $\left(\frac{\pi}{3}, 0\right)$ in rectangular coordinates

Find all the complex roots. Leave your answers in polar form with the argument in degrees. -The complex fifth roots of $\sqrt { 3 } + i$

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ). - $y = 5$

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( 1,2,0 ) , \mathrm { P } _ { 2 } ( - 2,3,2 ) , \mathrm { P } _ { 3 } ( 0 , - 2,3 )$

Find the value of the determinant. - $\left| \begin{array} { r r } - 6 & 9 \\- 7 & - 1\end{array} \right|$

Plot the point given in polar coordinates. - $\left. ( 2,360 ) ^ { 0 } \right)$ A) B) C) D)

Solve the problem. -If v = 3i - 5j and w = -7i + 4j, find 3v - 4w.