Find the angle between the two planes. $\begin{array} { l } x - 4 y + z = - 3 \\ 3 x + 3 z + 4 = 0 \end{array}$

A) 71.5 $^\circ$ B) 72.5 $^\circ$ C) 73.5 $^\circ$ D) 70.5 $^\circ$ E) 69.5 $^\circ$ A) 71.5 $^\circ$ B) 72.5 $^\circ$ C) 73.5 $^\circ$ D) 70.5 $^\circ$ E) 69.5 $^\circ$

Find the angle $\theta$ between the vectors.Round your answer to two decimal places. $\begin{array} { l } \mathbf { u } = 12 \mathbf { j } - 28 \mathbf { k } \\ \mathbf { v } = 14 \mathbf { i } - 9 \mathbf { k } \end{array}$

A) $\Theta \approx 58.20 ^ { \circ }$ B) $\Theta \approx 62.20 ^ { \circ }$ C) $\Theta \approx 59.20 ^ { \circ }$ D) $\Theta \approx 61.20 ^ { \circ }$ E) $\Theta \approx 60.20 ^ { \circ }$ A) $\Theta \approx 58.20 ^ { \circ }$ B) $\Theta \approx 62.20 ^ { \circ }$ C) $\Theta \approx 59.20 ^ { \circ }$ D) $\Theta \approx 61.20 ^ { \circ }$ E) $\Theta \approx 60.20 ^ { \circ }$

Find the dot product of u and v. $\begin{array} { l } \mathbf { u } = 7 \mathbf { i } - 10 \mathbf { j } + 8 \mathbf { k } \\ \mathbf { v } = 24 \mathbf { i } + 8 \mathbf { j } - \mathbf { k } \end{array}$

A) $ u^{.}v =$ 78 B) $ u^{.}v =$ 81 C) $ u^{.}v =$ 80 D) $ u^{.}v =$ 79 E) $ u^{.}v =$ 82 A) $ u^{.}v =$ 78 B) $ u^{.}v =$ 81 C) $ u^{.}v =$ 80 D) $ u^{.}v =$ 79 E) $ u^{.}v =$ 82

Exam 11: Analytic Geometry In Three Dimensions

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v,and w. =(9,9,0) =(0,0,-9) =(9,0,9) $Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v,and w. \begin{array} { l } \mathbf { u } = ( 9,9,0 ) \\ \mathbf { v } = ( 0,0 , - 9 ) \\ \mathbf { w } = ( 9,0,9 ) \end{array} \mathrm { a } = ( 9,9,0 ) , \mathrm { b } = ( 0,0 , - 9 ) , \mathrm { c } = ( 9,0,9 )$ $\mathrm { a } = ( 9,9,0 ) , \mathrm { b } = ( 0,0 , - 9 ) , \mathrm { c } = ( 9,0,9 )$

(Multiple Choice)

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Question 61

The vector v and its initial point are given.Find the terminal point. $v = ( 4 , - 6,9 )$ Initial point: $( 1,7,0 )$

(Multiple Choice)

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Question 62

Find the magnitude of v. $\mathbf { v } = 4 \mathbf { i } + \mathbf { j } - \mathbf { k }$

(Multiple Choice)

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Question 63

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: (0,0,0) Perpendicular to: $\mathbf { n } = - 2 \mathbf { j } + 6 \mathbf { k }$

(Multiple Choice)

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Question 64

Find a set of parametric equations for the line that passes through the given points. (8,2,3), (-1,3,-6)

(Essay)

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Question 65

Find a set of symmetric equations of the line that passes through the given points. $( - 5,8,12 ) , ( 1 , - 2,19 )$

(Multiple Choice)

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Question 66

Find the magnitude of v. $\mathbf { v } = 8 \mathbf { i } - 12 \mathbf { j } + \mathbf { k }$

(Multiple Choice)

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Question 67

Find the vector z,given u = $( 7,6 , - 5 )$ and v = $( 1,2 , - 6 )$ ,and w = $( - 21,26 , - 5 )$ . -3u+ 4v- 4z = w

(Multiple Choice)

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Question 68

Find the distance between the points. (-8,0,2,), (-3,-8,-7)

(Multiple Choice)

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Question 69

Find the angle between the two planes. x-4y+z=-3 3x+3z+4=0

(Multiple Choice)

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Question 70

Find a set of parametric equations for the line through the point and parallel to the specified vector or line.(For each line,write the direction numbers as integers. ) Point: $( 2,0,2 )$ Parallel to: $x = 3 + 4 t , y = 5 - 5 t , z = - 7 + 3 t$

(Multiple Choice)

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Question 71

Find the triple scalar product. $\mathbf { u } = ( 3,0,4 ) \mathbf { v } = ( 0,5,0 ) \mathbf { w } = ( 0,0,8 )$

(Multiple Choice)

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Question 72

Find the standard form of the equation of the sphere with the given characteristics. Center: $( - 5,5,1 )$ ;radius: 1

(Multiple Choice)

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Question 73

Find the dot product of u and v. u = $( 9 , - 9 , - 2 )$ ,v = $( - 9 , - 2 , - 9 )$

(Multiple Choice)

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Question 74

Find the vector z,given $\mathbf { u } = ( - 1,3,4 ) , \mathbf { v } = ( 1 , - 4 , - 4 )$ . $\mathbf { u } + \mathbf { v } + \mathbf { z } = 0$

(Multiple Choice)

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Question 75

Find a set of parametric equations for the line that passes through the given points. $\left( 6 , \frac { - 9 } { 2 } , \frac { - 5 } { 2 } \right) , \left( \frac { 3 } { 2 } , \frac { 1 } { 2 } , - 7 \right)$

(Essay)

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Question 76

Determine the octant(s)in which (x,y,z)is located so that the condition(s)is (are)satisfied. $z > 5$

(Multiple Choice)

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Question 77

Find the angle $\theta$ between the vectors.Round your answer to two decimal places. =12-28 =14-9

(Multiple Choice)

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Question 78

Find the midpoint of the line segment joining the points. $( 0 , - 5,4 ) , ( 3,2,5 )$

(Multiple Choice)

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Question 79

Find the dot product of u and v. =7-10+8 =24+8-

(Multiple Choice)

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Question 80

The vector v and its initial point are given.Find the terminal point. $v = ( 4 , - 6,9 )$ Initial point: $( 1,7,0 )$

Find the magnitude of v. $\mathbf { v } = 4 \mathbf { i } + \mathbf { j } - \mathbf { k }$

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: (0,0,0) Perpendicular to: $\mathbf { n } = - 2 \mathbf { j } + 6 \mathbf { k }$

Find a set of parametric equations for the line that passes through the given points. (8,2,3), (-1,3,-6)

Find a set of symmetric equations of the line that passes through the given points. $( - 5,8,12 ) , ( 1 , - 2,19 )$

Find the magnitude of v. $\mathbf { v } = 8 \mathbf { i } - 12 \mathbf { j } + \mathbf { k }$

Find the vector z,given u = $( 7,6 , - 5 )$ and v = $( 1,2 , - 6 )$ ,and w = $( - 21,26 , - 5 )$ . -3u+ 4v- 4z = w

Find the distance between the points. (-8,0,2,), (-3,-8,-7)

Find the angle between the two planes. x-4y+z=-3 3x+3z+4=0

Find a set of parametric equations for the line through the point and parallel to the specified vector or line.(For each line,write the direction numbers as integers. ) Point: $( 2,0,2 )$ Parallel to: $x = 3 + 4 t , y = 5 - 5 t , z = - 7 + 3 t$

Find the triple scalar product. $\mathbf { u } = ( 3,0,4 ) \mathbf { v } = ( 0,5,0 ) \mathbf { w } = ( 0,0,8 )$

Find the standard form of the equation of the sphere with the given characteristics. Center: $( - 5,5,1 )$ ;radius: 1

Find the dot product of u and v. u = $( 9 , - 9 , - 2 )$ ,v = $( - 9 , - 2 , - 9 )$

Find the vector z,given $\mathbf { u } = ( - 1,3,4 ) , \mathbf { v } = ( 1 , - 4 , - 4 )$ . $\mathbf { u } + \mathbf { v } + \mathbf { z } = 0$

Find a set of parametric equations for the line that passes through the given points. $\left( 6 , \frac { - 9 } { 2 } , \frac { - 5 } { 2 } \right) , \left( \frac { 3 } { 2 } , \frac { 1 } { 2 } , - 7 \right)$

Determine the octant(s)in which (x,y,z)is located so that the condition(s)is (are)satisfied. $z > 5$

Find the angle $\theta$ between the vectors.Round your answer to two decimal places. =12-28 =14-9

Find the midpoint of the line segment joining the points. $( 0 , - 5,4 ) , ( 3,2,5 )$

Find the dot product of u and v. =7-10+8 =24+8-

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Limits and An Introduction To Calculus

Filters

Exam 11: Analytic Geometry In Three Dimensions

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v,and w. =(9,9,0) =(0,0,-9) =(9,0,9) a=(9,9,0),b=(0,0,−9),c=(9,0,9)\mathrm { a } = ( 9,9,0 ) , \mathrm { b } = ( 0,0 , - 9 ) , \mathrm { c } = ( 9,0,9 )a=(9,9,0),b=(0,0,−9),c=(9,0,9)

The vector v and its initial point are given.Find the terminal point. v=(4,−6,9)v = ( 4 , - 6,9 )v=(4,−6,9) Initial point: (1,7,0)( 1,7,0 )(1,7,0)

Find the magnitude of v. v=4i+j−k\mathbf { v } = 4 \mathbf { i } + \mathbf { j } - \mathbf { k }v=4i+j−k

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: (0,0,0) Perpendicular to: n=−2j+6k\mathbf { n } = - 2 \mathbf { j } + 6 \mathbf { k }n=−2j+6k

Find a set of parametric equations for the line that passes through the given points. (8,2,3), (-1,3,-6)

Find a set of symmetric equations of the line that passes through the given points. (−5,8,12),(1,−2,19)( - 5,8,12 ) , ( 1 , - 2,19 )(−5,8,12),(1,−2,19)

Find the magnitude of v. v=8i−12j+k\mathbf { v } = 8 \mathbf { i } - 12 \mathbf { j } + \mathbf { k }v=8i−12j+k

Find the vector z,given u = (7,6,−5)( 7,6 , - 5 )(7,6,−5) and v = (1,2,−6)( 1,2 , - 6 )(1,2,−6) ,and w = (−21,26,−5)( - 21,26 , - 5 )(−21,26,−5) . -3u+ 4v- 4z = w

Find the distance between the points. (-8,0,2,), (-3,-8,-7)

Find the angle between the two planes. x-4y+z=-3 3x+3z+4=0

Find the triple scalar product. u=(3,0,4)v=(0,5,0)w=(0,0,8)\mathbf { u } = ( 3,0,4 ) \mathbf { v } = ( 0,5,0 ) \mathbf { w } = ( 0,0,8 )u=(3,0,4)v=(0,5,0)w=(0,0,8)

Find the standard form of the equation of the sphere with the given characteristics. Center: (−5,5,1)( - 5,5,1 )(−5,5,1) ;radius: 1

Find the dot product of u and v. u = (9,−9,−2)( 9 , - 9 , - 2 )(9,−9,−2) ,v = (−9,−2,−9)( - 9 , - 2 , - 9 )(−9,−2,−9)

Find the vector z,given u=(−1,3,4),v=(1,−4,−4)\mathbf { u } = ( - 1,3,4 ) , \mathbf { v } = ( 1 , - 4 , - 4 )u=(−1,3,4),v=(1,−4,−4) . u+v+z=0\mathbf { u } + \mathbf { v } + \mathbf { z } = 0u+v+z=0

Find a set of parametric equations for the line that passes through the given points. (6,−92,−52),(32,12,−7)\left( 6 , \frac { - 9 } { 2 } , \frac { - 5 } { 2 } \right) , \left( \frac { 3 } { 2 } , \frac { 1 } { 2 } , - 7 \right)(6,2−9​,2−5​),(23​,21​,−7)

Determine the octant(s)in which (x,y,z)is located so that the condition(s)is (are)satisfied. z>5z > 5z>5

Find the angle θ\thetaθ between the vectors.Round your answer to two decimal places. =12-28 =14-9

Find the midpoint of the line segment joining the points. (0,−5,4),(3,2,5)( 0 , - 5,4 ) , ( 3,2,5 )(0,−5,4),(3,2,5)

Find the dot product of u and v. =7-10+8 =24+8-

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Limits and An Introduction To Calculus

Filters

The vector v and its initial point are given.Find the terminal point. $v = ( 4 , - 6,9 )$ Initial point: $( 1,7,0 )$

Find the magnitude of v. $\mathbf { v } = 4 \mathbf { i } + \mathbf { j } - \mathbf { k }$

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: (0,0,0) Perpendicular to: $\mathbf { n } = - 2 \mathbf { j } + 6 \mathbf { k }$

Find a set of symmetric equations of the line that passes through the given points. $( - 5,8,12 ) , ( 1 , - 2,19 )$

Find the magnitude of v. $\mathbf { v } = 8 \mathbf { i } - 12 \mathbf { j } + \mathbf { k }$

Find the vector z,given u = $( 7,6 , - 5 )$ and v = $( 1,2 , - 6 )$ ,and w = $( - 21,26 , - 5 )$ . -3u+ 4v- 4z = w

Find the triple scalar product. $\mathbf { u } = ( 3,0,4 ) \mathbf { v } = ( 0,5,0 ) \mathbf { w } = ( 0,0,8 )$

Find the standard form of the equation of the sphere with the given characteristics. Center: $( - 5,5,1 )$ ;radius: 1

Find the dot product of u and v. u = $( 9 , - 9 , - 2 )$ ,v = $( - 9 , - 2 , - 9 )$

Find the vector z,given $\mathbf { u } = ( - 1,3,4 ) , \mathbf { v } = ( 1 , - 4 , - 4 )$ . $\mathbf { u } + \mathbf { v } + \mathbf { z } = 0$

Find a set of parametric equations for the line that passes through the given points. $\left( 6 , \frac { - 9 } { 2 } , \frac { - 5 } { 2 } \right) , \left( \frac { 3 } { 2 } , \frac { 1 } { 2 } , - 7 \right)$

Determine the octant(s)in which (x,y,z)is located so that the condition(s)is (are)satisfied. $z > 5$

Find the angle $\theta$ between the vectors.Round your answer to two decimal places. =12-28 =14-9

Find the midpoint of the line segment joining the points. $( 0 , - 5,4 ) , ( 3,2,5 )$