Exam 8: Polar Coordinates; Vectors

The rectangular coordinates of a point are given. Find polar coordinates for the point. - $( 100 , - 30 )$ Round the polar coordinates to two decimal places, with $\theta$ in degrees.

Solve the problem. Leave your answer in polar form. - z=1-i w=1-i Find $\frac { z } { w }$ .

Choose the one alternative that best completes the statement or answers the question. Find the direction angles of the vector. Round to the nearest degree, if necessary. - $\mathbf { v } = \mathbf { i } - \mathbf { j } + 2 \mathbf { k }$

Find the angle between v and w. Round your answer to one decimal place, if necessary. - $v = - 5 i + 7 \mathbf { j } , \quad \mathbf { w } = - 6 \mathbf { i } - 4 \mathbf { j }$

Choose the one alternative that best completes the statement or answers the question. The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( 5 , \frac { 3 \pi } { 4 } \right)$

Solve the problem. Round your answer to the nearest tenth. -A person is pulling a freight cart with a force of 40 pounds. How much work is done in moving the cart 30 feet if the cart's handle makes an angle of 22° with the ground?

Choose the one alternative that best completes the statement or answers the question. The polar coordinates of a point are given. Find the rectangular coordinates of the point. - $\left( 7 , \frac { 2 \pi } { 3 } \right)$

Write the complex number in rectangular form. - $8 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$

Find the distance from P1 to P2. - $\mathrm { P } _ { 1 } = ( 0,0,0 )$ and $\mathrm { P } _ { 2 } = ( 2,4,3 )$

Test the equation for symmetry with respect to the given axis, line, or pole. - $\mathrm { r } = 6 + 2 \cos \theta \text {; the pole }$

Find the indicated cross product. - $\mathbf { v } = 6 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k } , \quad \mathbf { w } = - 4 \mathbf { i } - 4 \mathbf { k }$ Find $v \times w$ .

Match the point in polar coordinates with either A, B, C, or D on the graph. - $\left( - 3 , - \frac { \pi } { 3 } \right)$

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - $r \sin \theta = 4$

Plot the point given in polar coordinates. - $\left( 4 , \frac { - 5 \pi } { 4 } \right)$

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Find a unit vector normal to the plane containing $\mathbf { u } = - \mathbf { i } + \mathbf { j } + 4 \mathbf { k } \text { and } \mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j } + \mathbf { k }$

Find the area of the parallelogram. - $\mathrm { P } _ { 1 } ( 0,0,0 ) , \mathrm { P } _ { 2 } ( 4,2,1 ) , \mathrm { P } _ { 3 } ( - 2,3,1 )$

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $- 6$

Find the dot product v · w. - $\mathbf { v } = 2 \mathbf { i } + \mathbf { j } + 3 \mathbf { k }$ and $\mathbf { w } = \mathrm { i } + 2 \mathbf { j } - 2 \mathbf { k }$

Graph the polar equation. - $r=\csc \theta-2,0<\theta<\pi$

Find the unit vector having the same direction as v. - $\mathbf { v } = - 3 \mathbf { i } + \mathbf { j }$