Find the dot product of u and v. $\begin{array} { l } \mathbf { u } = ( 7 , - 1,14 ) \\ \mathbf { v } = ( 8 , - 14,1 ) \end{array}$

A) $ u^{.}v =$ 85 B) $ u^{.}v =$ 84 C) $ u^{.}v =$ 82 D) $ u^{.}v =$ -86 E) $ u^{.}v =$ 14 A) $ u^{.}v =$ 85 B) $ u^{.}v =$ 84 C) $ u^{.}v =$ 82 D) $ u^{.}v =$ -86 E) $ u^{.}v =$ 14

Exam 11: Analytic Geometry In Three Dimensions

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: $( - 2,2,0 )$ Parallel to: $\mathbf { v } = \frac { 3 } { 7 } \mathrm { i } - \frac { 4 } { 7 } \mathbf { j } - 3 \mathrm { k }$

(Multiple Choice)

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Question 21

Use the vectors u and v to find (3u)× v. $\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }$

(Multiple Choice)

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Question 22

Find the vector z,given u = $( - 3 , - 2,9 )$ and v = $( 6 , - 3 , - 2 )$ . z = 4u - 4v

(Multiple Choice)

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Question 23

Determine whether u and v are parallel,orthogonal,or neither. u = $( 3,1 , - 16 )$ ,v = $( 5,1,1 )$

(Multiple Choice)

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Question 24

Find the coordinates of the point. The point is located four units in front of the yz-plane,five units to the left of the xz-plane,and six units below the xy-plane.

(Multiple Choice)

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Question 25

Find a unit vector orthogonal to u and v. $\mathbf { u } = ( - 2 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k } \quad \mathbf { v } = ( 3 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k }$

(Multiple Choice)

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Question 26

Find the distance between the points. $( 0,0,0 ) , ( 5,2,6 )$

(Multiple Choice)

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Question 27

Find the general form of the equation of the plane passing through the point and perpendicular to the specified line.[Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.] (-3,3,-7) x=4-t y=1-3t z=3-5t

(Multiple Choice)

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Question 28

Find the triple scalar product. $\mathbf { u } = ( 2,3,3 ) , \mathbf { v } = ( 1,2,0 ) , \mathbf { w } = ( 0,0,4 )$

(Multiple Choice)

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Question 29

Find the magnitude of the vector v. v = $( 8,6 , - 8 )$

(Multiple Choice)

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Question 30

Find the triple scalar product u · (v × w)for the vectors $\mathbf { u } = ( - 9 ) \mathbf { i } + ( 1 ) \mathbf { j } + ( - 7 ) \mathbf { k } , \mathbf { v } = ( 7 ) \mathbf { i } + ( - 1 ) \mathbf { j } + ( - 6 ) \mathbf { k } , w = ( - 7 ) \mathbf { i } + ( 4 ) \mathbf { j } + ( \# \# k$ ) K

(Multiple Choice)

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Question 31

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: (5,0,2) Parallel to: $x = 3 + 3 t , y = 5 - 2 t , z = - 7 + t$

(Multiple Choice)

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Question 32

Find a set of parametric equations for the line through the point and parallel to the specified line. $( - 4,8,8 )$ , parallel to x=7-5t y=-3-8t z=-2+3t

(Essay)

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Question 33

The vector v and its initial point are given.Find the terminal point. $v = ( 9 , - 1 , - 1 )$ Initial point: $( 16 , - 9,8 )$

(Multiple Choice)

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Question 34

Find the distance between the points. $( 1,0 , - 5 ) , ( 8,8,15 )$

(Multiple Choice)

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Question 35

Find the coordinates of the point. The point is located on the x-axis,four units in front of the yz-plane.

(Multiple Choice)

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Question 36

Find the distance between the points. $( 7 , - 7,3 ) , ( - 1 , - 4,7 )$

(Multiple Choice)

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Question 37

Use vectors to determine whether the points are collinear. (-9,-1,2), (-12,-3,-2), (-10,3,7)

(Multiple Choice)

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Question 38

Find the dot product of u and v. =(7,-1,14) =(8,-14,1)

(Multiple Choice)

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Question 39

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: $( 0,0,8 )$ Perpendicular to: $x = 1 - t , y = 2 + t , z = 4 - 4 t$

(Multiple Choice)

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Question 40

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: $( - 2,2,0 )$ Parallel to: $\mathbf { v } = \frac { 3 } { 7 } \mathrm { i } - \frac { 4 } { 7 } \mathbf { j } - 3 \mathrm { k }$

Use the vectors u and v to find (3u)× v. $\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }$

Find the vector z,given u = $( - 3 , - 2,9 )$ and v = $( 6 , - 3 , - 2 )$ . z = 4u - 4v

Determine whether u and v are parallel,orthogonal,or neither. u = $( 3,1 , - 16 )$ ,v = $( 5,1,1 )$

Find the coordinates of the point. The point is located four units in front of the yz-plane,five units to the left of the xz-plane,and six units below the xy-plane.

Find a unit vector orthogonal to u and v. $\mathbf { u } = ( - 2 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k } \quad \mathbf { v } = ( 3 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k }$

Find the distance between the points. $( 0,0,0 ) , ( 5,2,6 )$

Find the general form of the equation of the plane passing through the point and perpendicular to the specified line.[Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.] (-3,3,-7) x=4-t y=1-3t z=3-5t

Find the triple scalar product. $\mathbf { u } = ( 2,3,3 ) , \mathbf { v } = ( 1,2,0 ) , \mathbf { w } = ( 0,0,4 )$

Find the magnitude of the vector v. v = $( 8,6 , - 8 )$

Find the triple scalar product u · (v × w)for the vectors $\mathbf { u } = ( - 9 ) \mathbf { i } + ( 1 ) \mathbf { j } + ( - 7 ) \mathbf { k } , \mathbf { v } = ( 7 ) \mathbf { i } + ( - 1 ) \mathbf { j } + ( - 6 ) \mathbf { k } , w = ( - 7 ) \mathbf { i } + ( 4 ) \mathbf { j } + ( \# \# k$ ) K

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: (5,0,2) Parallel to: $x = 3 + 3 t , y = 5 - 2 t , z = - 7 + t$

Find a set of parametric equations for the line through the point and parallel to the specified line. $( - 4,8,8 )$ , parallel to x=7-5t y=-3-8t z=-2+3t

The vector v and its initial point are given.Find the terminal point. $v = ( 9 , - 1 , - 1 )$ Initial point: $( 16 , - 9,8 )$

Find the distance between the points. $( 1,0 , - 5 ) , ( 8,8,15 )$

Find the coordinates of the point. The point is located on the x-axis,four units in front of the yz-plane.

Find the distance between the points. $( 7 , - 7,3 ) , ( - 1 , - 4,7 )$

Use vectors to determine whether the points are collinear. (-9,-1,2), (-12,-3,-2), (-10,3,7)

Find the dot product of u and v. =(7,-1,14) =(8,-14,1)

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: $( 0,0,8 )$ Perpendicular to: $x = 1 - t , y = 2 + t , z = 4 - 4 t$

Functions and Their Graphs

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Exponential and Logarithmic Functions

Trigonometry

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Exam 11: Analytic Geometry In Three Dimensions

Use the vectors u and v to find (3u)× v. u=7i−j+8kv=6i+6j−k\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }u=7i−j+8kv=6i+6j−k

Find the vector z,given u = (−3,−2,9)( - 3 , - 2,9 )(−3,−2,9) and v = (6,−3,−2)( 6 , - 3 , - 2 )(6,−3,−2) . z = 4u - 4v

Determine whether u and v are parallel,orthogonal,or neither. u = (3,1,−16)( 3,1 , - 16 )(3,1,−16) ,v = (5,1,1)( 5,1,1 )(5,1,1)

Find the coordinates of the point. The point is located four units in front of the yz-plane,five units to the left of the xz-plane,and six units below the xy-plane.

Find a unit vector orthogonal to u and v. u=(−2)i+(8)j+(−1)kv=(3)i+(8)j+(−1)k\mathbf { u } = ( - 2 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k } \quad \mathbf { v } = ( 3 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k }u=(−2)i+(8)j+(−1)kv=(3)i+(8)j+(−1)k

Find the distance between the points. (0,0,0),(5,2,6)( 0,0,0 ) , ( 5,2,6 )(0,0,0),(5,2,6)

Find the general form of the equation of the plane passing through the point and perpendicular to the specified line.[Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.] (-3,3,-7) x=4-t y=1-3t z=3-5t

Find the triple scalar product. u=(2,3,3),v=(1,2,0),w=(0,0,4)\mathbf { u } = ( 2,3,3 ) , \mathbf { v } = ( 1,2,0 ) , \mathbf { w } = ( 0,0,4 )u=(2,3,3),v=(1,2,0),w=(0,0,4)

Find the magnitude of the vector v. v = (8,6,−8)( 8,6 , - 8 )(8,6,−8)

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: (5,0,2) Parallel to: x=3+3t,y=5−2t,z=−7+tx = 3 + 3 t , y = 5 - 2 t , z = - 7 + tx=3+3t,y=5−2t,z=−7+t

Find a set of parametric equations for the line through the point and parallel to the specified line. (−4,8,8)( - 4,8,8 )(−4,8,8) , parallel to x=7-5t y=-3-8t z=-2+3t

The vector v and its initial point are given.Find the terminal point. v=(9,−1,−1)v = ( 9 , - 1 , - 1 )v=(9,−1,−1) Initial point: (16,−9,8)( 16 , - 9,8 )(16,−9,8)

Find the distance between the points. (1,0,−5),(8,8,15)( 1,0 , - 5 ) , ( 8,8,15 )(1,0,−5),(8,8,15)

Find the coordinates of the point. The point is located on the x-axis,four units in front of the yz-plane.

Find the distance between the points. (7,−7,3),(−1,−4,7)( 7 , - 7,3 ) , ( - 1 , - 4,7 )(7,−7,3),(−1,−4,7)

Use vectors to determine whether the points are collinear. (-9,-1,2), (-12,-3,-2), (-10,3,7)

Find the dot product of u and v. =(7,-1,14) =(8,-14,1)

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: (0,0,8)( 0,0,8 )(0,0,8) Perpendicular to: x=1−t,y=2+t,z=4−4tx = 1 - t , y = 2 + t , z = 4 - 4 tx=1−t,y=2+t,z=4−4t

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

Use the vectors u and v to find (3u)× v. $\mathbf { u } = 7 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } \quad \mathbf { v } = 6 \mathbf { i } + 6 \mathbf { j } - \mathbf { k }$

Find the vector z,given u = $( - 3 , - 2,9 )$ and v = $( 6 , - 3 , - 2 )$ . z = 4u - 4v

Determine whether u and v are parallel,orthogonal,or neither. u = $( 3,1 , - 16 )$ ,v = $( 5,1,1 )$

Find a unit vector orthogonal to u and v. $\mathbf { u } = ( - 2 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k } \quad \mathbf { v } = ( 3 ) \mathbf { i } + ( 8 ) \mathbf { j } + ( - 1 ) \mathbf { k }$

Find the distance between the points. $( 0,0,0 ) , ( 5,2,6 )$

Find the triple scalar product. $\mathbf { u } = ( 2,3,3 ) , \mathbf { v } = ( 1,2,0 ) , \mathbf { w } = ( 0,0,4 )$

Find the magnitude of the vector v. v = $( 8,6 , - 8 )$

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. Point: (5,0,2) Parallel to: $x = 3 + 3 t , y = 5 - 2 t , z = - 7 + t$

Find a set of parametric equations for the line through the point and parallel to the specified line. $( - 4,8,8 )$ , parallel to x=7-5t y=-3-8t z=-2+3t

The vector v and its initial point are given.Find the terminal point. $v = ( 9 , - 1 , - 1 )$ Initial point: $( 16 , - 9,8 )$

Find the distance between the points. $( 1,0 , - 5 ) , ( 8,8,15 )$

Find the distance between the points. $( 7 , - 7,3 ) , ( - 1 , - 4,7 )$

Find the general form of the equation of the plane passing through the point and perpendicular to the specified vector or line. Point: $( 0,0,8 )$ Perpendicular to: $x = 1 - t , y = 2 + t , z = 4 - 4 t$