Find the area of the parallelogram that has the vectors as adjacent sides. $\begin{array} { l } \mathbf { u } = ( 9,9 , - 11 ) \\ \mathbf { v } = ( 9,0,11 ) \end{array}$

A) $\text { Area } = \sqrt { 45,864.00 } \text { square untis }$ B) $\text { Area } = \sqrt { 6,858.00 } \text { square untis }$ C) $\text { Area } = \sqrt { 378.00 } \text { square untis }$ D) $\text { Area } = \sqrt { 55,566.00 } \text { square untis }$ E) $\text { Area } = \sqrt { 42444.00 } \text { square untis }$ A) $\text { Area } = \sqrt { 45,864.00 } \text { square untis }$ B) $\text { Area } = \sqrt { 6,858.00 } \text { square untis }$ C) $\text { Area } = \sqrt { 378.00 } \text { square untis }$ D) $\text { Area } = \sqrt { 55,566.00 } \text { square untis }$ E) $\text { Area } = \sqrt { 42444.00 } \text { square untis }$

Find the angle $\Theta$ between the vectors.Round your answer to two decimal places. $\begin{array} { l } \mathbf { u } = ( 0,4,4 ) \\ \mathbf { v } = ( 5,0 , - 6 ) \end{array}$

A) $\Theta \approx 122.90 ^ { \circ }$ B) $\Theta \approx 123.90 ^ { \circ }$ C) $\Theta \approx 121.90 ^ { \circ }$ D) $\Theta \approx 124.90 ^ { \circ }$ E) $\Theta \approx 120.90 ^ { \circ }$ A) $\Theta \approx 122.90 ^ { \circ }$ B) $\Theta \approx 123.90 ^ { \circ }$ C) $\Theta \approx 121.90 ^ { \circ }$ D) $\Theta \approx 124.90 ^ { \circ }$ E) $\Theta \approx 120.90 ^ { \circ }$

Exam 11: Analytic Geometry In Three Dimensions

Find the general form of the equation of the plane passing through the three points.[Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.] (-4,4,-1), (1,6,2), (-5,-3,6)

(Multiple Choice)

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Question 181

Find symmetric equations for the line through the point and parallel to the specified line. $( - 7,6 , - 8 )$ , parallel to x=-4-4t y=-2+2t z=1-5t

(Essay)

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Question 182

Determine the octant(s)in which (x,y,z)is located so that the conditions are satisfied. x > 0,y > 0,z > 0

(Multiple Choice)

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Question 183

Find the midpoint of the line segment joining the points. $( - 1,3,8 ) , ( 9 , - 4,3 )$

(Multiple Choice)

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Question 184

A spherical building has a diameter of $201$ feet.The center of the building is placed at the origin of a three-dimensional coordinate system.What is the equation of the sphere?

(Multiple Choice)

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Question 185

Find the area of the parallelogram that has the vectors as adjacent sides. =(9,9,-11) =(9,0,11)

(Multiple Choice)

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Question 186

Find the standard form of the equation of the sphere with the given characteristics. Center: $( 7,0 , - 14 )$ ;diameter: 14

(Multiple Choice)

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Question 187

Determine whether u and v are parallel,orthogonal,or neither. u = $( 1,9 , - 2 )$ ,v = $( 2,0,1 )$

(Multiple Choice)

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Question 188

Find the magnitude of the vector described below. Initial point: (-3,7,-5) Terminal point: (8,-3,4)

(Multiple Choice)

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Question 189

Determine whether the planes are parallel,orthogonal,or neither. 5x - y + z = -4 -x - 6y - z = -2

(Multiple Choice)

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Question 190

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: (0,0,0) Parallel to: $\mathbf { v } = ( 5,6,7 )$

(Multiple Choice)

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Question 191

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: $( 3,2,6 )$ Perpendicular to: $n = i$

(Multiple Choice)

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Question 192

Find the magnitude of v. $\mathbf { v } = - 3 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }$

(Multiple Choice)

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Question 193

Find the angle $\Theta$ between the vectors.Round your answer to two decimal places. =(0,4,4) =(5,0,-6)

(Multiple Choice)

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Question 194

Find the angle of intersection of the planes in degrees.Round to a tenth of a degree. 3x + 2y - 6z = -5 -6x + 3y + z = 1

(Multiple Choice)

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Question 195

Find the angle between the two planes in degrees.Round to a tenth of a degree. 3x - 4y + z = -6 2x + y + 3z = 0

(Multiple Choice)

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Question 196

Find a unit vector in the direction opposite of u. $\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }$

(Multiple Choice)

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Question 197

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: $( 6 , - 2,2 )$ Parallel to: $\mathbf { v } = ( 3 , - 4 , - 10 )$

(Multiple Choice)

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Question 198

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v,and w. =++5 =5+5 =5+5 $Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v,and w. \begin{array} { l } \mathbf { u } = \mathbf { i } + \mathbf { j } + 5 \mathbf { k } \\ \mathbf { v } = 5 \mathbf { j } + 5 \mathbf { k } \\ \mathbf { w } = 5 \mathbf { i } + 5 \mathbf { k } \end{array} \mathrm { a } = ( 1,1,5 ) , \mathrm { b } = ( 0,5,5 ) , \mathrm { c } = ( 5,0,5 )$ $\mathrm { a } = ( 1,1,5 ) , \mathrm { b } = ( 0,5,5 ) , \mathrm { c } = ( 5,0,5 )$

(Multiple Choice)

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Question 199

Find a unit vector in the direction of u $\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$

(Multiple Choice)

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Question 200

Showing 181 - 200 of 256

Find the general form of the equation of the plane passing through the three points.[Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.] (-4,4,-1), (1,6,2), (-5,-3,6)

Find symmetric equations for the line through the point and parallel to the specified line. $( - 7,6 , - 8 )$ , parallel to x=-4-4t y=-2+2t z=1-5t

Determine the octant(s)in which (x,y,z)is located so that the conditions are satisfied. x > 0,y > 0,z > 0

Find the midpoint of the line segment joining the points. $( - 1,3,8 ) , ( 9 , - 4,3 )$

A spherical building has a diameter of $201$ feet.The center of the building is placed at the origin of a three-dimensional coordinate system.What is the equation of the sphere?

Find the area of the parallelogram that has the vectors as adjacent sides. =(9,9,-11) =(9,0,11)

Find the standard form of the equation of the sphere with the given characteristics. Center: $( 7,0 , - 14 )$ ;diameter: 14

Determine whether u and v are parallel,orthogonal,or neither. u = $( 1,9 , - 2 )$ ,v = $( 2,0,1 )$

Find the magnitude of the vector described below. Initial point: (-3,7,-5) Terminal point: (8,-3,4)

Determine whether the planes are parallel,orthogonal,or neither. 5x - y + z = -4 -x - 6y - z = -2

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: (0,0,0) Parallel to: $\mathbf { v } = ( 5,6,7 )$

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: $( 3,2,6 )$ Perpendicular to: $n = i$

Find the magnitude of v. $\mathbf { v } = - 3 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }$

Find the angle $\Theta$ between the vectors.Round your answer to two decimal places. =(0,4,4) =(5,0,-6)

Find the angle of intersection of the planes in degrees.Round to a tenth of a degree. 3x + 2y - 6z = -5 -6x + 3y + z = 1

Find the angle between the two planes in degrees.Round to a tenth of a degree. 3x - 4y + z = -6 2x + y + 3z = 0

Find a unit vector in the direction opposite of u. $\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }$

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: $( 6 , - 2,2 )$ Parallel to: $\mathbf { v } = ( 3 , - 4 , - 10 )$

Find a unit vector in the direction of u $\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$

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

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Exam 11: Analytic Geometry In Three Dimensions

Find the general form of the equation of the plane passing through the three points.[Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.] (-4,4,-1), (1,6,2), (-5,-3,6)

Find symmetric equations for the line through the point and parallel to the specified line. (−7,6,−8)( - 7,6 , - 8 )(−7,6,−8) , parallel to x=-4-4t y=-2+2t z=1-5t

Determine the octant(s)in which (x,y,z)is located so that the conditions are satisfied. x > 0,y > 0,z > 0 ​

Find the midpoint of the line segment joining the points. (−1,3,8),(9,−4,3)( - 1,3,8 ) , ( 9 , - 4,3 )(−1,3,8),(9,−4,3)

A spherical building has a diameter of 201201201 feet.The center of the building is placed at the origin of a three-dimensional coordinate system.What is the equation of the sphere?

Find the area of the parallelogram that has the vectors as adjacent sides. =(9,9,-11) =(9,0,11)

Find the standard form of the equation of the sphere with the given characteristics. Center: (7,0,−14)( 7,0 , - 14 )(7,0,−14) ;diameter: 14

Determine whether u and v are parallel,orthogonal,or neither. u = (1,9,−2)( 1,9 , - 2 )(1,9,−2) ,v = (2,0,1)( 2,0,1 )(2,0,1)

Find the magnitude of the vector described below. Initial point: (-3,7,-5) Terminal point: (8,-3,4)

Determine whether the planes are parallel,orthogonal,or neither. 5x - y + z = -4 -x - 6y - z = -2

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: (0,0,0) Parallel to: v=(5,6,7)\mathbf { v } = ( 5,6,7 )v=(5,6,7)

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: (3,2,6)( 3,2,6 )(3,2,6) Perpendicular to: n=in = in=i

Find the magnitude of v. v=−3i−2j+k\mathbf { v } = - 3 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }v=−3i−2j+k

Find the angle Θ\ThetaΘ between the vectors.Round your answer to two decimal places. =(0,4,4) =(5,0,-6)

Find the angle of intersection of the planes in degrees.Round to a tenth of a degree. 3x + 2y - 6z = -5 -6x + 3y + z = 1

Find the angle between the two planes in degrees.Round to a tenth of a degree. 3x - 4y + z = -6 2x + y + 3z = 0

Find a unit vector in the direction opposite of u. u=9i+4j−k\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }u=9i+4j−k

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: (6,−2,2)( 6 , - 2,2 )(6,−2,2) Parallel to: v=(3,−4,−10)\mathbf { v } = ( 3 , - 4 , - 10 )v=(3,−4,−10)

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u,v,and w. =++5 =5+5 =5+5 a=(1,1,5),b=(0,5,5),c=(5,0,5)\mathrm { a } = ( 1,1,5 ) , \mathrm { b } = ( 0,5,5 ) , \mathrm { c } = ( 5,0,5 )a=(1,1,5),b=(0,5,5),c=(5,0,5)

Find a unit vector in the direction of u u=10i+5j−k\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }u=10i+5j−k

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

Find symmetric equations for the line through the point and parallel to the specified line. $( - 7,6 , - 8 )$ , parallel to x=-4-4t y=-2+2t z=1-5t

Determine the octant(s)in which (x,y,z)is located so that the conditions are satisfied. x > 0,y > 0,z > 0

Find the midpoint of the line segment joining the points. $( - 1,3,8 ) , ( 9 , - 4,3 )$

A spherical building has a diameter of $201$ feet.The center of the building is placed at the origin of a three-dimensional coordinate system.What is the equation of the sphere?

Find the standard form of the equation of the sphere with the given characteristics. Center: $( 7,0 , - 14 )$ ;diameter: 14

Determine whether u and v are parallel,orthogonal,or neither. u = $( 1,9 , - 2 )$ ,v = $( 2,0,1 )$

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: (0,0,0) Parallel to: $\mathbf { v } = ( 5,6,7 )$

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: $( 3,2,6 )$ Perpendicular to: $n = i$

Find the magnitude of v. $\mathbf { v } = - 3 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }$

Find the angle $\Theta$ between the vectors.Round your answer to two decimal places. =(0,4,4) =(5,0,-6)

Find a unit vector in the direction opposite of u. $\mathbf { u } = 9 \mathbf { i } + 4 \mathbf { j } - \mathbf { k }$

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: $( 6 , - 2,2 )$ Parallel to: $\mathbf { v } = ( 3 , - 4 , - 10 )$

Find a unit vector in the direction of u $\mathbf { u } = 10 \mathbf { i } + 5 \mathbf { j } - \mathbf { k }$