Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } z = 6 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right) \\ w = 12 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \end{array}\] Find $\frac { Z } { W }$.

A) $\frac { 1 } { 6 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ B) $\frac { 1 } { 6 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ C) $\frac { 1 } { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ D) $\frac { 1 } { 2 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ A) $\frac { 1 } { 6 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$ B) $\frac { 1 } { 6 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ C) $\frac { 1 } { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right)$ D) $\frac { 1 } { 2 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Perform the indicated operation. -\[\begin{array} { l } \mathbf { v } = 3 \mathbf { i } + 5 \mathbf { j } - 2 \mathbf { k } \text { and } \mathbf { w } = 2 \mathbf { i } - 4 \mathbf { j } + 6 \mathbf { k } \\ \text { Find } \| \mathbf { v } - \| \mathbf { w } \| \\ \end{array}\]

A) $\sqrt {154 }$ B) $\sqrt { 138}-$ $2\sqrt {14 }$ C) $\sqrt { 146}$ D) $3 \sqrt { 2 }-6$ A) $\sqrt {154 }$ B) $\sqrt { 138}-$ $2\sqrt {14 }$ C) $\sqrt { 146}$ D) $3 \sqrt { 2 }-6$

Solve the problem. Leave your answer in polar form. -\[\begin{array} { l } z = 5 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) \\ w = 4 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) \end{array}\] Find $\frac { z } { w }$.

A) $\frac { 4 } { 5 } \left( \cos 40 ^ { \circ } + \mathrm { i } \sin 40 ^ { \circ } \right)$ B) $\frac { 4 } { 5 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ C) $\frac { 5 } { 4 } \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ D) $\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ A) $\frac { 4 } { 5 } \left( \cos 40 ^ { \circ } + \mathrm { i } \sin 40 ^ { \circ } \right)$ B) $\frac { 4 } { 5 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ C) $\frac { 5 } { 4 } \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$ D) $\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$

Exam 8: Polar Coordinates; Vectors

Perform the indicated operation. - $\mathbf { v } = - 5 \mathbf { i } - 4 \mathbf { j } - 3 \mathbf { k }$ and $\mathbf { w } = 3 \mathbf { i } - 2 \mathbf { j } + 6 \mathbf { k }$ Find $\| \mathbf { v } - \mathbf { w } \|$ .

(Multiple Choice)

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Question 101

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find $\frac { Z } { W }$ .

(Multiple Choice)

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Question 102

Find the angle between v and w. Round your answer to one decimal place, if necessary. - $\mathbf { v } = 4 \mathbf { i } + 7 \mathbf { j }$ , $\mathbf { w } = 3 \mathbf { i } + 8 \mathbf { j }$

(Multiple Choice)

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Question 103

Perform the indicated operation. - =3+5-2 and =2-4+6 Find \|-\|\|

(Multiple Choice)

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Question 104

Describe the set of points (x, y, z) defined by the equation. -x = -2 and z = -4

(Multiple Choice)

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Question 105

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -A DC-10 jumbo jet maintains an airspeed of 600 miles per hour in a southeasterly direction. The velocity of the jet stream is a constant 50 miles per hour from the west. Find the actual speed and direction of the aircraft. (Round the speed and direction to the nearest tenth.)

(Short Answer)

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Question 106

Plot the point given in polar coordinates. - $\left( 5 , \frac { 5 \pi } { 3 } \right)$ $Plot the point given in polar coordinates. - \left( 5 , \frac { 5 \pi } { 3 } \right)$

(Multiple Choice)

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Question 107

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Plot the point $\left( 4 , \frac { \pi } { 6 } \right)$ and find other polar coordinates $( r , \theta )$ of the point for which: (a) $\mathrm { r } > 0 , \quad - 2 \pi \leq \theta < 0$ (b) $\mathrm { r } < 0 , \quad 0 \leq \theta < 2 \pi$ (c) $\mathrm { r } > 0 \quad 2 \pi \leq \theta < 4 \pi$ $Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Plot the point \left( 4 , \frac { \pi } { 6 } \right) and find other polar coordinates ( r , \theta ) of the point for which: (a) \mathrm { r } > 0 , \quad - 2 \pi \leq \theta < 0 (b) \mathrm { r } < 0 , \quad 0 \leq \theta < 2 \pi (c) \mathrm { r } > 0 \quad 2 \pi \leq \theta < 4 \pi$

(Essay)

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Question 108

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. - $\left( - 5,120 ^ { \circ } \right)$

(Multiple Choice)

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Question 109

Find the unit vector having the same direction as v. - $\mathbf { v } = - 30 \mathbf { i } + 30 \mathbf { j } - 15 \mathbf { k }$

(Multiple Choice)

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Question 110

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. - $\mathrm { P } = ( 4,4 ) ; \mathrm { Q } = ( - 3 , - 6 )$

(Multiple Choice)

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Question 111

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

(Multiple Choice)

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Question 112

Find the value of the determinant. - $\left| \begin{array} { r r } - 1 & 1 \\ 2 & 3 \end{array} \right|$

(Multiple Choice)

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Question 113

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. - $\left( - 5 , - 360 ^ { \circ } \right)$

(Multiple Choice)

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Question 114

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

(Multiple Choice)

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Question 115

Perform the indicated operation. - $\mathbf { v } = 4 \mathbf { i } - 5 \mathbf { j } + 6 \mathbf { k } \text { and } \mathbf { w } = 3 \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k }$ Find $3 v + 2 w$ .

(Multiple Choice)

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Question 116

Solve the problem. Leave your answer in polar form. - z=5 20+i20 w=4 5+i5 Find $\frac { z } { w }$ .

(Multiple Choice)

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Question 117

Perform the indicated operation. - $v = 6 i + 4 j + 3 k$ and $w = 5 i + 2 j - 6 k$ Find $4 v - 3 w$ .

(Multiple Choice)

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Question 118

Plot the complex number in the complex plane. - $-3-i$

(Multiple Choice)

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Question 119

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

(Multiple Choice)

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Question 120

Showing 101 - 120 of 253

Perform the indicated operation. - $\mathbf { v } = - 5 \mathbf { i } - 4 \mathbf { j } - 3 \mathbf { k }$ and $\mathbf { w } = 3 \mathbf { i } - 2 \mathbf { j } + 6 \mathbf { k }$ Find $\| \mathbf { v } - \mathbf { w } \|$ .

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find $\frac { Z } { W }$ .

Find the angle between v and w. Round your answer to one decimal place, if necessary. - $\mathbf { v } = 4 \mathbf { i } + 7 \mathbf { j }$ , $\mathbf { w } = 3 \mathbf { i } + 8 \mathbf { j }$

Perform the indicated operation. - =3+5-2 and =2-4+6 Find \|-\|\|

Describe the set of points (x, y, z) defined by the equation. -x = -2 and z = -4

Plot the point given in polar coordinates. - $\left( 5 , \frac { 5 \pi } { 3 } \right)$ $Plot the point given in polar coordinates. - \left( 5 , \frac { 5 \pi } { 3 } \right)$

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. - $\left( - 5,120 ^ { \circ } \right)$

Find the unit vector having the same direction as v. - $\mathbf { v } = - 30 \mathbf { i } + 30 \mathbf { j } - 15 \mathbf { k }$

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. - $\mathrm { P } = ( 4,4 ) ; \mathrm { Q } = ( - 3 , - 6 )$

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

Find the value of the determinant. - $\left| \begin{array} { r r } - 1 & 1 \\ 2 & 3 \end{array} \right|$

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. - $\left( - 5 , - 360 ^ { \circ } \right)$

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

Perform the indicated operation. - $\mathbf { v } = 4 \mathbf { i } - 5 \mathbf { j } + 6 \mathbf { k } \text { and } \mathbf { w } = 3 \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k }$ Find $3 v + 2 w$ .

Solve the problem. Leave your answer in polar form. - z=5 20+i20 w=4 5+i5 Find $\frac { z } { w }$ .

Perform the indicated operation. - $v = 6 i + 4 j + 3 k$ and $w = 5 i + 2 j - 6 k$ Find $4 v - 3 w$ .

Plot the complex number in the complex plane. - $-3-i$

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

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 8: Polar Coordinates; Vectors

Perform the indicated operation. - v=−5i−4j−3k\mathbf { v } = - 5 \mathbf { i } - 4 \mathbf { j } - 3 \mathbf { k }v=−5i−4j−3k and w=3i−2j+6k\mathbf { w } = 3 \mathbf { i } - 2 \mathbf { j } + 6 \mathbf { k }w=3i−2j+6k Find ∥v−w∥\| \mathbf { v } - \mathbf { w } \|∥v−w∥ .

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find ZW\frac { Z } { W }WZ​ .

Find the angle between v and w. Round your answer to one decimal place, if necessary. - v=4i+7j\mathbf { v } = 4 \mathbf { i } + 7 \mathbf { j }v=4i+7j , w=3i+8j\mathbf { w } = 3 \mathbf { i } + 8 \mathbf { j }w=3i+8j

Perform the indicated operation. - =3+5-2 and =2-4+6 Find \|-\|\|

Describe the set of points (x, y, z) defined by the equation. -x = -2 and z = -4

Plot the point given in polar coordinates. - (5,5π3)\left( 5 , \frac { 5 \pi } { 3 } \right)(5,35π​)

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. - (−5,120∘)\left( - 5,120 ^ { \circ } \right)(−5,120∘)

Find the unit vector having the same direction as v. - v=−30i+30j−15k\mathbf { v } = - 30 \mathbf { i } + 30 \mathbf { j } - 15 \mathbf { k }v=−30i+30j−15k

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. - P=(4,4);Q=(−3,−6)\mathrm { P } = ( 4,4 ) ; \mathrm { Q } = ( - 3 , - 6 )P=(4,4);Q=(−3,−6)

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

Find the value of the determinant. - ∣−1123∣\left| \begin{array} { r r } - 1 & 1 \\ 2 & 3 \end{array} \right|​−12​13​​

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. - (−5,−360∘)\left( - 5 , - 360 ^ { \circ } \right)(−5,−360∘)

Test the equation for symmetry with respect to the given axis, line, or pole. - r=2sin⁡θr = 2 \sin \thetar=2sinθ ; the pole

Perform the indicated operation. - v=4i−5j+6k and w=3i−4j+2k\mathbf { v } = 4 \mathbf { i } - 5 \mathbf { j } + 6 \mathbf { k } \text { and } \mathbf { w } = 3 \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k }v=4i−5j+6k and w=3i−4j+2k Find 3v+2w3 v + 2 w3v+2w .

Solve the problem. Leave your answer in polar form. - z=5 20+i20 w=4 5+i5 Find zw\frac { z } { w }wz​ .

Perform the indicated operation. - v=6i+4j+3kv = 6 i + 4 j + 3 kv=6i+4j+3k and w=5i+2j−6kw = 5 i + 2 j - 6 kw=5i+2j−6k Find 4v−3w4 v - 3 w4v−3w .

Plot the complex number in the complex plane. - −3−i-3-i−3−i

Solve the problem. -If v=3i−5jv = 3 i - 5 jv=3i−5j and w=−7i+4jw = - 7 i + 4 jw=−7i+4j , find 3v−4w3 v - 4 w3v−4w .

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Perform the indicated operation. - $\mathbf { v } = - 5 \mathbf { i } - 4 \mathbf { j } - 3 \mathbf { k }$ and $\mathbf { w } = 3 \mathbf { i } - 2 \mathbf { j } + 6 \mathbf { k }$ Find $\| \mathbf { v } - \mathbf { w } \|$ .

Solve the problem. Leave your answer in polar form. - z=6 +i w=12 +i Find $\frac { Z } { W }$ .

Find the angle between v and w. Round your answer to one decimal place, if necessary. - $\mathbf { v } = 4 \mathbf { i } + 7 \mathbf { j }$ , $\mathbf { w } = 3 \mathbf { i } + 8 \mathbf { j }$

Plot the point given in polar coordinates. - $\left( 5 , \frac { 5 \pi } { 3 } \right)$ $Plot the point given in polar coordinates. - \left( 5 , \frac { 5 \pi } { 3 } \right)$

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. - $\left( - 5,120 ^ { \circ } \right)$

Find the unit vector having the same direction as v. - $\mathbf { v } = - 30 \mathbf { i } + 30 \mathbf { j } - 15 \mathbf { k }$

The vector v has initial position P and terminal point Q. Write v in the form ai + bj; that is, find its position vector. - $\mathrm { P } = ( 4,4 ) ; \mathrm { Q } = ( - 3 , - 6 )$

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

Find the value of the determinant. - $\left| \begin{array} { r r } - 1 & 1 \\ 2 & 3 \end{array} \right|$

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. - $\left( - 5 , - 360 ^ { \circ } \right)$

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

Perform the indicated operation. - $\mathbf { v } = 4 \mathbf { i } - 5 \mathbf { j } + 6 \mathbf { k } \text { and } \mathbf { w } = 3 \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k }$ Find $3 v + 2 w$ .

Solve the problem. Leave your answer in polar form. - z=5 20+i20 w=4 5+i5 Find $\frac { z } { w }$ .

Perform the indicated operation. - $v = 6 i + 4 j + 3 k$ and $w = 5 i + 2 j - 6 k$ Find $4 v - 3 w$ .

Plot the complex number in the complex plane. - $-3-i$

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