Question 1

Write the component form of the vector described below. Initial point: (3,8,-3)
Terminal point: (-9,5,-4)

Accepted Answer

A)  $( - 12,12 , - 1 )$ 
B)  $( - 12,1 , - 1 )$ 
C)  $( - 7 , - 3 , - 1 )$ 
D)  $( - 12 , - 3,1 )$ 
E)  $( - 12 , - 3 , - 1 )$ 
A)  $( - 12,12 , - 1 )$ 
B)  $( - 12,1 , - 1 )$ 
C)  $( - 7 , - 3 , - 1 )$ 
D)  $( - 12 , - 3,1 )$ 
E)  $( - 12 , - 3 , - 1 )$

Question 2

Find a set of parametric equations of the line. 
Passes through $( - 1,6 , - 3 )$ and is parallel to $\mathbf { v } = 5 \mathbf { i } - \mathbf { j }$ .

Accepted Answer

A)  $\begin{array} { l } 
x = - 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$ 
B)  $\begin{array} { l } 
x = - 1 + 5 t \
y = - 6 - t \
z = - 3
\end{array}$ 
C)  $\begin{array} { l } 
x = 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$ 
D)  $\begin{array} { l } 
x = - 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$ 
E)  $\begin{array} { l } 
x = 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$ 
A)  $\begin{array} { l } 
x = - 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$ 
B)  $\begin{array} { l } 
x = - 1 + 5 t \
y = - 6 - t \
z = - 3
\end{array}$ 
C)  $\begin{array} { l } 
x = 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$ 
D)  $\begin{array} { l } 
x = - 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$ 
E)  $\begin{array} { l } 
x = 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$

Question 3

Find the distance between the point and the plane. 
(-5,-6,-5) $$2 x + 3 y - 9 z = - 1$$

Accepted Answer

A) 18 
B)  $\frac { 18 } { 94 }$ 
C)  $\frac { 1 } { \sqrt { 94 } }$ 
D) 0 
E)  $\frac { 18 } { \sqrt { 94 } }$ 
A) 18 
B)  $\frac { 18 } { 94 }$ 
C)  $\frac { 1 } { \sqrt { 94 } }$ 
D) 0 
E)  $\frac { 18 } { \sqrt { 94 } }$

Question 4

Find the distance between the points. $( 4 , - 2,0 ) , ( 0,4 , - 1 )$

Accepted Answer

A)  $\sqrt { 53 }$ units 
B)  $\sqrt { 57 }$ units 
C)  $2 \sqrt { 14 }$ units 
D)  $\sqrt { 55 }$ units 
E)  $3 \sqrt { 6 }$ units 
A)  $\sqrt { 53 }$ units 
B)  $\sqrt { 57 }$ units 
C)  $2 \sqrt { 14 }$ units 
D)  $\sqrt { 55 }$ units 
E)  $3 \sqrt { 6 }$ units

Question 5

Find the midpoint of the line segment joining the points.  $( 4 , - 1,7 ) , ( - 5,2,2 )$

Accepted Answer

A) ( $- \frac { 1 } { 2 }$ , $\frac { 1 } { 2 }$ , $\frac { 9 } { 2 }$ ) 
B) ( $\frac { 1 } { 2 }$ , $\frac { 9 } { 2 }$ , $- \frac { 1 } { 2 }$ ) 
C) ( $\frac { 9 } { 2 }$ , $\frac { 1 } { 2 }$ , $- \frac { 1 } { 2 }$ ) 
D) ( $\frac { 1 } { 2 }$ , $- \frac { 1 } { 2 }$ ,- $\frac { 9 } { 2 }$ ) 
E) ( $\frac { 9 } { 2 }$ , $- \frac { 1 } { 2 }$ , $\frac { 1 } { 2 }$ ) 
A) ( $- \frac { 1 } { 2 }$ , $\frac { 1 } { 2 }$ , $\frac { 9 } { 2 }$ ) 
B) ( $\frac { 1 } { 2 }$ , $\frac { 9 } { 2 }$ , $- \frac { 1 } { 2 }$ ) 
C) ( $\frac { 9 } { 2 }$ , $\frac { 1 } { 2 }$ , $- \frac { 1 } { 2 }$ ) 
D) ( $\frac { 1 } { 2 }$ , $- \frac { 1 } { 2 }$ ,- $\frac { 9 } { 2 }$ ) 
E) ( $\frac { 9 } { 2 }$ , $- \frac { 1 } { 2 }$ , $\frac { 1 } { 2 }$ )

Question 6

Find the midpoint of the line segment joining the points. (8,-4,-2), (-3,-9,-7)

Accepted Answer

A)  $\left( \frac { 11 } { 2 } , \frac { 5 } { 2 } , \frac { 5 } { 2 } \right)$ 
B)  $\left( \frac { 5 } { 2 } , \frac { - 13 } { 2 } , \frac { - 9 } { 2 } \right)$ 
C)  $( 5 , - 13 , - 9 )$ 
D)  $( 11,5,5 )$ 
E)  $( 11,0 , - 9 )$ 
A)  $\left( \frac { 11 } { 2 } , \frac { 5 } { 2 } , \frac { 5 } { 2 } \right)$ 
B)  $\left( \frac { 5 } { 2 } , \frac { - 13 } { 2 } , \frac { - 9 } { 2 } \right)$ 
C)  $( 5 , - 13 , - 9 )$ 
D)  $( 11,5,5 )$ 
E)  $( 11,0 , - 9 )$

Question 7

Find the distance between the points.  $( 1,0,0 ) , ( 7,0,4 )$

Accepted Answer

A) 8.06 units 
B) 9.22 units 
C) 3.61 units 
D) 4.47 units 
E) 7.21 units 
A) 8.06 units 
B) 9.22 units 
C) 3.61 units 
D) 4.47 units 
E) 7.21 units

Question 8

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

Accepted Answer

A) 167.7° 
B) -80.6° 
C) 170.6° 
D) 44.6° 
E) 3.0° 
A) 167.7° 
B) -80.6° 
C) 170.6° 
D) 44.6° 
E) 3.0°

Question 9

Find the lengths of the sides of the triangle with the indicated vertices.  $( 1 , - 4,5 ) , ( - 5,1,3 ) , ( 5,4,0 )$

Accepted Answer

A) d1= $\sqrt { 65 }$ ,d2= $\sqrt { 118 }$ ,d3= $\sqrt { 105 }$ 
B) d1= $\sqrt { 118 }$ ,d2= $\sqrt { 105 }$ ,d3= $\sqrt { 118 }$ 
C) d1= $\sqrt { 105 }$ ,d2= $\sqrt { 105 }$ ,d3= $\sqrt { 118 }$ 
D) d1= $\sqrt { 65 }$ ,d2= $\sqrt { 65 }$ ,d3= $\sqrt { 118 }$ 
E) d1= $\sqrt { 65 }$ ,d2= $\sqrt { 105 }$ ,d3= $\sqrt { 65 }$ 
A) d1= $\sqrt { 65 }$ ,d2= $\sqrt { 118 }$ ,d3= $\sqrt { 105 }$ 
B) d1= $\sqrt { 118 }$ ,d2= $\sqrt { 105 }$ ,d3= $\sqrt { 118 }$ 
C) d1= $\sqrt { 105 }$ ,d2= $\sqrt { 105 }$ ,d3= $\sqrt { 118 }$ 
D) d1= $\sqrt { 65 }$ ,d2= $\sqrt { 65 }$ ,d3= $\sqrt { 118 }$ 
E) d1= $\sqrt { 65 }$ ,d2= $\sqrt { 105 }$ ,d3= $\sqrt { 65 }$

Question 10

Find the angle between the vectors u and v.Express your answer in degrees and round to the nearest tenth of a degree. u = -6i - 7j + 4k,v = 4i - 4j + 6k

Accepted Answer

A) 18.7° 
B) 19.7° 
C) 71.3° 
D) 90° 
E) 70.3° 
A) 18.7° 
B) 19.7° 
C) 71.3° 
D) 90° 
E) 70.3°

Question 11

Find the angle between the two planes in degrees.Round to a tenth of a degree. 
5x - 6y - 4z = -5
X + y + 5z = -1

Accepted Answer

A) 114.5° 
B) 27.4° 
C) 117.4° 
D) 24.7° 
E) 2.0° 
A) 114.5° 
B) 27.4° 
C) 117.4° 
D) 24.7° 
E) 2.0°

Question 12

Find the lengths of the sides of the triangle with the indicated vertices.  $( 0,0,4 ) , ( - 4,3,4 ) , ( 0,4,0 )$

Accepted Answer

A) d1= $4 \sqrt { 2 }$ ,d2= $4 \sqrt { 2 }$ ,d3= $\sqrt { 33 }$ 
B) d1= $5$ ,d2= $4 \sqrt { 2 }$ ,d3= $5$ 
C) d1= $5$ ,d2= $4 \sqrt { 2 }$ ,d3= $\sqrt { 33 }$ 
D) d1= $5$ ,d2= $5$ ,d3= $\sqrt { 33 }$ 
E) d1= $\sqrt { 33 }$ ,d2= $4 \sqrt { 2 }$ ,d3= $\sqrt { 33 }$ 
A) d1= $4 \sqrt { 2 }$ ,d2= $4 \sqrt { 2 }$ ,d3= $\sqrt { 33 }$ 
B) d1= $5$ ,d2= $4 \sqrt { 2 }$ ,d3= $5$ 
C) d1= $5$ ,d2= $4 \sqrt { 2 }$ ,d3= $\sqrt { 33 }$ 
D) d1= $5$ ,d2= $5$ ,d3= $\sqrt { 33 }$ 
E) d1= $\sqrt { 33 }$ ,d2= $4 \sqrt { 2 }$ ,d3= $\sqrt { 33 }$

Question 13

Write the component form of the vector v. 
Initial point: $( - 9,7 , - 5 )$ Terminal point: $( 1 , - 1,6 )$

Accepted Answer

A)  $v =$ $( - 8 , - 8,11 )$ 
B)  $v =$ $( 11 , - 8,10 )$ 
C)  $v =$ $( 10 , - 8,11 )$ 
D)  $v =$ $( - 8,10,11 )$ 
E)  $v =$ $( 10,11 , - 8 )$ 
A)  $v =$ $( - 8 , - 8,11 )$ 
B)  $v =$ $( 11 , - 8,10 )$ 
C)  $v =$ $( 10 , - 8,11 )$ 
D)  $v =$ $( - 8,10,11 )$ 
E)  $v =$ $( 10,11 , - 8 )$

Question 14

Find the magnitude of v.  $\mathbf { v } = 5 \mathbf { i } - 4 \mathbf { j } - 8 \mathbf { k }$

Accepted Answer

A)  $\| v \| =$ $5 \sqrt { 2 }$ 
B)  $\| v \| =$ $\sqrt { 89 }$ 
C)  $\| v \| =$ $\sqrt { 41 }$ 
D)  $\| v \| =$ $\sqrt { 2.72 }$ 
E)  $\| v \| =$ $\sqrt { 105 }$ 
A)  $\| v \| =$ $5 \sqrt { 2 }$ 
B)  $\| v \| =$ $\sqrt { 89 }$ 
C)  $\| v \| =$ $\sqrt { 41 }$ 
D)  $\| v \| =$ $\sqrt { 2.72 }$ 
E)  $\| v \| =$ $\sqrt { 105 }$

Question 15

Find the angle $\Theta$ between the vectors.Round your answer to two decimal places.  $\begin{array} { l } 
\mathbf { u } = ( - 1,4,0 ) \
\mathbf { v } = ( 1,3 , - 1 )
\end{array}$

Accepted Answer

A)  $\Theta \approx 34.45 ^ { \circ }$ 
B)  $\Theta \approx 38.45 ^ { \circ }$ 
C)  $\Theta \approx 35.45 ^ { \circ }$ 
D)  $\Theta \approx 37.45 ^ { \circ }$ 
E)  $\Theta \approx 36.45 ^ { \circ }$ 
A)  $\Theta \approx 34.45 ^ { \circ }$ 
B)  $\Theta \approx 38.45 ^ { \circ }$ 
C)  $\Theta \approx 35.45 ^ { \circ }$ 
D)  $\Theta \approx 37.45 ^ { \circ }$ 
E)  $\Theta \approx 36.45 ^ { \circ }$

Question 16

Find the volume of the parallelepiped with the given vertices.  $\mathrm { A } ( 0,0,0 ) , \mathrm { B } ( 6,0,0 ) , \mathrm { C } ( 6 , - 4,5 ) , \mathrm { D } ( 0 , - 4,5 ) , \mathrm { E } ( 6,7,5 ) , \mathrm { F } ( 0,7,5 ) , \mathrm { G } ( 0,7,8 ) , \mathrm { H } ( 6,5,8 )$

Accepted Answer

A)  $\text { Volume } = 331 \text { cubic units }$ 
B)  $\text { Volume } = 332 \text { cubic units }$ 
C)  $\text { Volume } = 329 \text { cubic units }$ 
D)  $\text { Volume } = 330 \text { cubic units }$ 
E)  $\text { Volume } = 328 \text { cubic units }$ 
A)  $\text { Volume } = 331 \text { cubic units }$ 
B)  $\text { Volume } = 332 \text { cubic units }$ 
C)  $\text { Volume } = 329 \text { cubic units }$ 
D)  $\text { Volume } = 330 \text { cubic units }$ 
E)  $\text { Volume } = 328 \text { cubic units }$

Question 17

Find the general form of the equation of the plane passing through the three points.  $( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )$

Accepted Answer

A)  $- 7 x + 71 y + 77 z = 0$ 
B)  $- 7 x - 77 y - 71 z = 0$ 
C)  $- 7 x - 77 y + 71 z = 0$ 
D)  $- 7 x + 77 y - 71 z = 0$ 
E)  $- 7 x + 77 y + 71 z = 0$ 
A)  $- 7 x + 71 y + 77 z = 0$ 
B)  $- 7 x - 77 y - 71 z = 0$ 
C)  $- 7 x - 77 y + 71 z = 0$ 
D)  $- 7 x + 77 y - 71 z = 0$ 
E)  $- 7 x + 77 y + 71 z = 0$

Question 18

Find a set of parametric equations of the line. 
Passes through $( - 4,2,3 )$ and is parallel to the xy-plane and the yz-plane

Accepted Answer

A)  $\begin{array} { l } 
x = - 4 \
y = 2 \
z = 3 + t
\end{array}$ 
B)  $\begin{array} { l } 
x = - 4 + t \
y = 2 \
z = 3
\end{array}$ 
C)  $\begin{array} { l } 
x = - 4 \
y = 2 + t \
z = 3 + t
\end{array}$ 
D)  $\begin{array} { l } 
x = - 4 \
y = 2 + t \
z = 3
\end{array}$ 
E)  $\begin{array} { l } 
x = - 4 \
y = 2 \
z = 3 - t
\end{array}$ 
A)  $\begin{array} { l } 
x = - 4 \
y = 2 \
z = 3 + t
\end{array}$ 
B)  $\begin{array} { l } 
x = - 4 + t \
y = 2 \
z = 3
\end{array}$ 
C)  $\begin{array} { l } 
x = - 4 \
y = 2 + t \
z = 3 + t
\end{array}$ 
D)  $\begin{array} { l } 
x = - 4 \
y = 2 + t \
z = 3
\end{array}$ 
E)  $\begin{array} { l } 
x = - 4 \
y = 2 \
z = 3 - t
\end{array}$

Question 19

Find the magnitude of v.  $\mathbf { v } = ( - 4,0 , - 7 )$

Accepted Answer

A)  $\| \mathbf { v } \|$ = $\sqrt { 4.72 }$ 
B)  $\| \mathbf { v } \|$ = $\sqrt { 65 }$ 
C)  $\| \mathbf { v } \|$ = $\sqrt { 67 }$ 
D)  $\| \mathbf { v } \|$ = $4 \sqrt { 2 }$ 
E)  $\| \mathbf { v } \|$ = $\sqrt { 2.72 }$ 
A)  $\| \mathbf { v } \|$ = $\sqrt { 4.72 }$ 
B)  $\| \mathbf { v } \|$ = $\sqrt { 65 }$ 
C)  $\| \mathbf { v } \|$ = $\sqrt { 67 }$ 
D)  $\| \mathbf { v } \|$ = $4 \sqrt { 2 }$ 
E)  $\| \mathbf { v } \|$ = $\sqrt { 2.72 }$

Question 20

Find a unit vector in the opposite direction of u. u = $( - 14 , - 3,14 )$

Accepted Answer

A)  $\frac { \sqrt { 31 } } { \sqrt { 401 } } ( - 14 , - 3,14 )$ 
B)  $\sqrt { 401 } ( 14,3 , - 14 )$ 
C)  $( - 14 , - 3,14 )$ 
D)  $\frac { 1 } { \sqrt { 401 } } ( 14,3 , - 14 )$ 
E)  $\frac { 1 } { \sqrt { 31 } } ( - 14 , - 3,14 )$ 
A)  $\frac { \sqrt { 31 } } { \sqrt { 401 } } ( - 14 , - 3,14 )$ 
B)  $\sqrt { 401 } ( 14,3 , - 14 )$ 
C)  $( - 14 , - 3,14 )$ 
D)  $\frac { 1 } { \sqrt { 401 } } ( 14,3 , - 14 )$ 
E)  $\frac { 1 } { \sqrt { 31 } } ( - 14 , - 3,14 )$

Write the component form of the vector described below. Initial point: (3,8,-3) Terminal point: (-9,5,-4)

Find a set of parametric equations of the line. Passes through $( - 1,6 , - 3 )$ and is parallel to $\mathbf { v } = 5 \mathbf { i } - \mathbf { j }$ .

Find the distance between the point and the plane. (-5,-6,-5) $2 x + 3 y - 9 z = - 1$

Find the distance between the points. $( 4 , - 2,0 ) , ( 0,4 , - 1 )$

Find the midpoint of the line segment joining the points. $( 4 , - 1,7 ) , ( - 5,2,2 )$

Find the midpoint of the line segment joining the points. (8,-4,-2), (-3,-9,-7)

Find the distance between the points. $( 1,0,0 ) , ( 7,0,4 )$

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

Find the lengths of the sides of the triangle with the indicated vertices. $( 1 , - 4,5 ) , ( - 5,1,3 ) , ( 5,4,0 )$

Find the angle between the vectors u and v.Express your answer in degrees and round to the nearest tenth of a degree. u = -6i - 7j + 4k,v = 4i - 4j + 6k

Find the angle between the two planes in degrees.Round to a tenth of a degree. 5x - 6y - 4z = -5 X + y + 5z = -1

Find the lengths of the sides of the triangle with the indicated vertices. $( 0,0,4 ) , ( - 4,3,4 ) , ( 0,4,0 )$

Write the component form of the vector v. Initial point: $( - 9,7 , - 5 )$ Terminal point: $( 1 , - 1,6 )$

Find the magnitude of v. $\mathbf { v } = 5 \mathbf { i } - 4 \mathbf { j } - 8 \mathbf { k }$

Find the angle $\Theta$ between the vectors.Round your answer to two decimal places. =(-1,4,0) =(1,3,-1)

Find the volume of the parallelepiped with the given vertices. $\mathrm { A } ( 0,0,0 ) , \mathrm { B } ( 6,0,0 ) , \mathrm { C } ( 6 , - 4,5 ) , \mathrm { D } ( 0 , - 4,5 ) , \mathrm { E } ( 6,7,5 ) , \mathrm { F } ( 0,7,5 ) , \mathrm { G } ( 0,7,8 ) , \mathrm { H } ( 6,5,8 )$

Find the general form of the equation of the plane passing through the three points. $( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )$

Find a set of parametric equations of the line. Passes through $( - 4,2,3 )$ and is parallel to the xy-plane and the yz-plane

Find the magnitude of v. $\mathbf { v } = ( - 4,0 , - 7 )$

Find a unit vector in the opposite direction of u. u = $( - 14 , - 3,14 )$

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

Write the component form of the vector described below. Initial point: (3,8,-3) Terminal point: (-9,5,-4)

Find a set of parametric equations of the line. Passes through (−1,6,−3)( - 1,6 , - 3 )(−1,6,−3) and is parallel to v=5i−j\mathbf { v } = 5 \mathbf { i } - \mathbf { j }v=5i−j .

Find the distance between the point and the plane. (-5,-6,-5) 2x+3y−9z=−12 x + 3 y - 9 z = - 12x+3y−9z=−1

Find the distance between the points. (4,−2,0),(0,4,−1)( 4 , - 2,0 ) , ( 0,4 , - 1 )(4,−2,0),(0,4,−1)

Find the midpoint of the line segment joining the points. (4,−1,7),(−5,2,2)( 4 , - 1,7 ) , ( - 5,2,2 )(4,−1,7),(−5,2,2)

Find the midpoint of the line segment joining the points. (8,-4,-2), (-3,-9,-7)

Find the distance between the points. (1,0,0),(7,0,4)( 1,0,0 ) , ( 7,0,4 )(1,0,0),(7,0,4)

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

Find the lengths of the sides of the triangle with the indicated vertices. (1,−4,5),(−5,1,3),(5,4,0)( 1 , - 4,5 ) , ( - 5,1,3 ) , ( 5,4,0 )(1,−4,5),(−5,1,3),(5,4,0)

Find the angle between the vectors u and v.Express your answer in degrees and round to the nearest tenth of a degree. u = -6i - 7j + 4k,v = 4i - 4j + 6k

Find the angle between the two planes in degrees.Round to a tenth of a degree. 5x - 6y - 4z = -5 X + y + 5z = -1

Find the lengths of the sides of the triangle with the indicated vertices. (0,0,4),(−4,3,4),(0,4,0)( 0,0,4 ) , ( - 4,3,4 ) , ( 0,4,0 )(0,0,4),(−4,3,4),(0,4,0)

Write the component form of the vector v. Initial point: (−9,7,−5)( - 9,7 , - 5 )(−9,7,−5) Terminal point: (1,−1,6)( 1 , - 1,6 )(1,−1,6)

Find the magnitude of v. v=5i−4j−8k\mathbf { v } = 5 \mathbf { i } - 4 \mathbf { j } - 8 \mathbf { k }v=5i−4j−8k

Find the angle Θ\ThetaΘ between the vectors.Round your answer to two decimal places. =(-1,4,0) =(1,3,-1)

Find the general form of the equation of the plane passing through the three points. (0,0,0),(5,6,7),(−6,7,7)( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )(0,0,0),(5,6,7),(−6,7,7)

Find a set of parametric equations of the line. Passes through (−4,2,3)( - 4,2,3 )(−4,2,3) and is parallel to the xy-plane and the yz-plane

Find the magnitude of v. v=(−4,0,−7)\mathbf { v } = ( - 4,0 , - 7 )v=(−4,0,−7)

Find a unit vector in the opposite direction of u. u = (−14,−3,14)( - 14 , - 3,14 )(−14,−3,14)

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 a set of parametric equations of the line. Passes through $( - 1,6 , - 3 )$ and is parallel to $\mathbf { v } = 5 \mathbf { i } - \mathbf { j }$ .

Find the distance between the point and the plane. (-5,-6,-5) $2 x + 3 y - 9 z = - 1$

Find the distance between the points. $( 4 , - 2,0 ) , ( 0,4 , - 1 )$

Find the midpoint of the line segment joining the points. $( 4 , - 1,7 ) , ( - 5,2,2 )$

Find the distance between the points. $( 1,0,0 ) , ( 7,0,4 )$

Find the lengths of the sides of the triangle with the indicated vertices. $( 1 , - 4,5 ) , ( - 5,1,3 ) , ( 5,4,0 )$

Find the lengths of the sides of the triangle with the indicated vertices. $( 0,0,4 ) , ( - 4,3,4 ) , ( 0,4,0 )$

Write the component form of the vector v. Initial point: $( - 9,7 , - 5 )$ Terminal point: $( 1 , - 1,6 )$

Find the magnitude of v. $\mathbf { v } = 5 \mathbf { i } - 4 \mathbf { j } - 8 \mathbf { k }$

Find the angle $\Theta$ between the vectors.Round your answer to two decimal places. =(-1,4,0) =(1,3,-1)

Find the general form of the equation of the plane passing through the three points. $( 0,0,0 ) , ( 5,6,7 ) , ( - 6,7,7 )$

Find a set of parametric equations of the line. Passes through $( - 4,2,3 )$ and is parallel to the xy-plane and the yz-plane

Find the magnitude of v. $\mathbf { v } = ( - 4,0 , - 7 )$

Find a unit vector in the opposite direction of u. u = $( - 14 , - 3,14 )$