Exam 8: Polar Coordinates; Vectors

Find the angle between v and w. Round to one decimal place, if necessary. - $\mathbf { v } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$ and $\mathbf { w } = \mathbf { i } + 3 \mathbf { j } - 3 \mathbf { k }$

Graph the polar equation. - $\mathrm { r } = \tan \theta _ { , } - \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$

Write the expression in the standard form a + bi. - $( - \sqrt { 3 } + i ) ^ { 6 }$

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

Describe the set of points (x, y, z) defined by the equation. -z = 0

Graph the polar equation. - $r=\theta, \theta \geq 0$

Find the indicated cross product. - $\mathbf { v } = 5 \mathbf { i } - 6 \mathbf { j } , \quad \mathbf { w } = 3 \mathbf { i } + 2 \mathbf { j } - 2 \mathbf { k }$ Find $\mathbf { w } \times \mathbf { v }$ .

Solve the problem. Round your answer to the nearest tenth. -Find the work done by a force of 6 pounds acting in the direction of 43° to the horizontal in moving an object 6 feet from (0, 0) to (6, 0).

Match the graph to one of the polar equations. -

Choose the one alternative that best completes the statement or answers the question. -A box of supplies that weighs 1500 kilograms is suspended by two cables as shown in the figure. To two decimal places, what is the tension in the two cables?

Use the figure below. Determine whether the given statement is true or false. -C + D + G + I + J = 0

Write the expression in the standard form a + bi. - $\left[ \sqrt { 3 } \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \right] ^ { 4 }$

Use the given vectors to find the indicated expression. - $\mathbf { v } = - 4 \mathbf { i } + 2 \mathbf { j } - 3 \mathbf { k } , \quad \mathbf { u } = - 4 \mathbf { i } - 3 \mathbf { j } + 4 \mathbf { k }$ Find $\mathbf { v } \times ( - 5 \mathbf { u } )$ .