Exam 8: Polar Coordinates; Vectors

Match the point in polar coordinates with either A, B, C, or D on the graph. - $\left(3,-\frac{5 \pi}{3}\right)$

Use the figure below. Determine whether the given statement is true or false. -A + H = F

Use the vectors in the figure below to graph the following vector. - $2 \mathbf { u } - \mathbf { z } - \mathbf { w }$

Match the graph to one of the polar equations. -

Use the given vectors to find the indicated expression. - $\mathbf { v } = - 3 \mathbf { i } + 2 \mathbf { j } + \mathbf { k } , \quad \mathbf { w } = - 4 \mathbf { i } + 3 \mathbf { j } - \mathbf { k }$ Find $( - 3 \mathbf { v } ) \times \mathbf { w }$ .

Choose the one alternative that best completes the statement or answers the question. -Which of the following vectors is parallel to $\mathbf { v } = - 10 \mathbf { i } - 8 \mathbf { j }$ ?

The rectangular coordinates of a point are given. Find polar coordinates for the point. - $( - 3,3 )$

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

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

Write the vector v in the form ai + bj, given its magnitude v and the angle  it makes with the positive x-axis. - $\| \mathbf { v } \| = 15 , \alpha = 210 ^ { \circ }$

Match the graph to one of the polar equations. -

$36.86 \mathbf { i } + 25.81 \mathbf { j }$ -Two forces, $\mathbf { F } _ { 1 }$ of magnitude 35 newtons $( \mathrm { N } )$ and $\mathbf { F } _ { 2 }$ of magnitude 55 newtons, act on an object at angles of $45 ^ { \circ }$ and $- 60 ^ { \circ }$ (respectively) with the positive $x$ -axis. Find the direction and magnitude of the resultant force; that is, find $\mathbf { F } _ { 1 } + \mathbf { F } _ { 2 }$ . Round the direction and magnitude to two decimal places.

Choose the one alternative that best completes the statement or answers the question. Find the requested vector. - $\mathbf { v } = - 3 \mathbf { i } - 5 \mathbf { j } + \mathbf { k }$ Find a vector orthogonal to both $\mathbf { v }$ and $i + j$ .

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

Write the complex number in rectangular form. - $3 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Choose the one alternative that best completes the statement or answers the question. -Two forces of magnitude 25 pounds and 40 pounds act on an object. The force of $40 \mathrm { lb }$ acts along the positive $\mathrm { x }$ -axis, and the force of $25 \mathrm { lb }$ acts at an angle of $80 ^ { \circ }$ with the positive $x$ -axis. Find the direction and magnitude of the resultant force. Round the direction and magnitude to the nearest whole number.

State whether the vectors are parallel, orthogonal, or neither. - $\mathbf { v } = 2 \mathbf { i } - \mathbf { j } , \quad \mathbf { w } = 4 \mathbf { i } - 2 \mathbf { j }$

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $- 5 i$

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

Solve the problem. -If $\mathbf { v } = 9 \mathbf { i } + 3 \mathbf { j }$ , what is $\| 8 \mathbf { v } \|$ ?