Exam 8: Polar Coordinates; Vectors

The rectangular coordinates of a point are given. Find polar coordinates for the point. - $( 0.6 , - 1.1 )$ Round the polar coordinates to two decimal places, with $\theta$ in degrees.

Plot the point given in polar coordinates. - $\left( 4,315 ^ { \circ } \right)$

Find the unit vector having the same direction as v. - $\mathbf { v } = 7 \mathrm { i }$

Use the figure below. Determine whether the given statement is true or false. -A + B + C + D + E = 0

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -A sail on a sailboat is supported by a mast and a boom. The length and direction of the mast and boom can be described by the vectors , respectively, where the components are in meters. $\mathbf { m } = \mathbf { i } - 4 \mathbf { j } + 5 \mathbf { k } \text { and } \mathbf { b } = - 2 \mathbf { i } + 3 \mathbf { j } + \mathbf { k }$ Find the angle (to the nearest tenth of a degree) between the mast and boom.

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

Plot the point given in polar coordinates. - $\left(-2, \frac{-3 \pi}{4}\right)$

The rectangular coordinates of a point are given. Find polar coordinates for the point. - $( \sqrt { 3 } , - 1 )$

Write the expression in the standard form a + bi. - $\left[ 2 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right) \right] ^ { 3 }$

Choose the one alternative that best completes the statement or answers the question. Find the requested vector. - $\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j } + \mathbf { k } , \quad \mathbf { u } = - 2 \mathbf { i } + 2 \mathbf { j } - 2 \mathbf { k }$ Find a vector orthogonal to both $\mathbf { v }$ and $\mathbf { u }$ .

Find the quantity if v = 5i - 7j and w = 3i + 2j. - $\| v \| - \| w \|$

Find the area of the parallelogram with vertices P1, P2, P3, and P4. - $P _ { 1 } = ( 7 , - 5,5 ) , \quad P _ { 2 } = ( 4,7 , - 5 ) , \quad P _ { 3 } = ( 6,4 , - 2 ) , \quad P _ { 4 } = ( 3,16 , - 12 )$

Solve the problem. -If $\mathrm { P } = ( - 6 , - 9 )$ and $\mathrm { Q } = ( \mathrm { x } , - 105 )$ , find all numbers $\mathrm { x }$ such that the vector represented by $\overrightarrow { \mathrm { PQ } }$ has length $- 120$ .

Graph the polar equation. - $r = \frac { 4 } { 4 - 2 \sin \theta }$

Find the quantity if v = 5i - 7j and w = 3i + 2j. - $\| \mathrm { v } + \mathrm { w } \|$

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - $r=6 \cos \theta$

Match the graph to one of the polar equations. -

Graph the polar equation. - $r=\frac{3}{\theta}$

Write the expression in the standard form a + bi. - $\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) ^ { 10 }$

Choose the one alternative that best completes the statement or answers the question. -Which of the following vectors is orthogonal to $20 \mathbf { i } - 8 \mathbf { j }$ ?