Question 1

Determine the values of $c$ such that $\| c \mathbf { u } \| = 6$, where $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } - 5 \mathbf { k }$.

Accepted Answer

A)  $c = \pm 6$ 
B)  $c = \pm \frac { 3 \sqrt { 38 } } { 19 }$ 
C)  $c = \pm \frac { \sqrt { 38 } } { 6 }$ 
D)  $c = \pm \frac { 1 } { 6 }$ 
E)  $c = \pm \frac { \sqrt { 38 } } { 38 }$ 
A)  $c = \pm 6$ 
B)  $c = \pm \frac { 3 \sqrt { 38 } } { 19 }$ 
C)  $c = \pm \frac { \sqrt { 38 } } { 6 }$ 
D)  $c = \pm \frac { 1 } { 6 }$ 
E)  $c = \pm \frac { \sqrt { 38 } } { 38 }$

Question 2

Find the standard form of the equation of the sphere with the given characteristics.
Endpoints of a diameter: $( - 8,4 , - 2 ) , ( - 8 , - 2,6 )$

Accepted Answer

A)  $( x + 16 ) ^ { 2 } + ( x - 2 ) ^ { 2 } + ( x - 4 ) ^ { 2 } = 25$ 
B)  $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 50$ 
C)  $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 100$ 
D)  $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 25$ 
E)  $( x - 8 ) ^ { 2 } + ( x + 1 ) ^ { 2 } + ( x + 2 ) ^ { 2 } = 25$ 
A)  $( x + 16 ) ^ { 2 } + ( x - 2 ) ^ { 2 } + ( x - 4 ) ^ { 2 } = 25$ 
B)  $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 50$ 
C)  $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 100$ 
D)  $( x + 8 ) ^ { 2 } + ( x - 1 ) ^ { 2 } + ( x - 2 ) ^ { 2 } = 25$ 
E)  $( x - 8 ) ^ { 2 } + ( x + 1 ) ^ { 2 } + ( x + 2 ) ^ { 2 } = 25$

Question 3

Find the volume of the parallelpiped with the given vertices. $A ( 8 , - 5 , - 4 ) , B ( 2,2,5 ) , C ( 9,4 , - 12 ) , D ( 3,11 , - 3 )$,
$$E ( 8 , - 6 , - 10 ) , F ( 2,1 , - 1 ) , G ( 9,3 , - 18 ) , H ( 3,10 , - 9 )$$

Accepted Answer

A)  369 
B)  405 
C)  321 
D)  455 
E)  430 
A)  369 
B)  405 
C)  321 
D)  455 
E)  430

Question 4

Find the cross product of the unit vectors $k \times i$.

Accepted Answer

A)  $j$ 
B)  $- \mathrm { j }$ 
C)  $\mathrm { i }$ 
D)  $- \mathrm { i }$ 
E)  $k$ 
A)  $j$ 
B)  $- \mathrm { j }$ 
C)  $\mathrm { i }$ 
D)  $- \mathrm { i }$ 
E)  $k$

Question 5

Find a set of parametric equations for the line that passes through the given points. Show all your work.
$$\left( 4 , \frac { 9 } { 2 } , \frac { - 3 } { 2 } \right) , \left( \frac { 1 } { 2 } , \frac { - 3 } { 2 } , - 2 \right)$$

Accepted Answer

10. Answers may vary

Question 6

Find the coordinates of the point located three units in front of the $y z$-plane, eight units to the right of the $x z$-plane, and five units above the $x y$-plane.

Accepted Answer

A)  $( 3,5,8 )$ 
B)  $( 3,8,5 )$ 
C)  $( 3 , - 8,5 )$ 
D)  $( 3,5 , - 8 )$ 
E)  $( 3,11,16 )$ 
A)  $( 3,5,8 )$ 
B)  $( 3,8,5 )$ 
C)  $( 3 , - 8,5 )$ 
D)  $( 3,5 , - 8 )$ 
E)  $( 3,11,16 )$

Question 7

Find a set of parametric equations for the line that passes through the given points. Show all your work.
$$( 9,8 , - 2 ) , ( - 3 , - 6,4 )$$

Accepted Answer

Answers may vary. On

Question 8

Find the vector $\mathbf { z }$, given $\mathbf { u } = \langle - 4,9,8 \rangle , \mathbf { v } = \langle 5,4,4 \rangle$, and $\mathbf { w } = \langle - 3,23,4 \rangle$.
$3 \mathbf { u } - \mathbf { v } + 2 \mathbf { z } = \mathbf { w }$

Accepted Answer

A)  $\langle 14,0 , - 16 \rangle$ 
B)  $\langle 0,7 , - 8 \rangle$ 
C)  $\langle - 7,0 , - 8 \rangle$ 
D)  $\langle 7,0 , - 8 \rangle$ 
E)  $\langle 8,0 , - 7 \rangle$ 
A)  $\langle 14,0 , - 16 \rangle$ 
B)  $\langle 0,7 , - 8 \rangle$ 
C)  $\langle - 7,0 , - 8 \rangle$ 
D)  $\langle 7,0 , - 8 \rangle$ 
E)  $\langle 8,0 , - 7 \rangle$

Question 9

Find the magnitude of the vector $\mathbf { v }$.
$$\mathbf { v } = \langle 0 , - 4 , - 4 \rangle$$

Accepted Answer

A)  $- 8$ 
B)  8 
C)  $2 \sqrt { 2 }$ 
D)  $8 \sqrt { 2 }$ 
E)  $4 \sqrt { 2 }$ 
A)  $- 8$ 
B)  8 
C)  $2 \sqrt { 2 }$ 
D)  $8 \sqrt { 2 }$ 
E)  $4 \sqrt { 2 }$

Question 10

Find the acute interior angle of the parallelogram formed by $A ( 2 , - 2,2 )$, $B ( 5 , - 1,4 ) , C ( 6,0,10 )$, and $D ( 3 , - 1,8 )$. Round your answer to two decimals.

Accepted Answer

A)  $43.92 ^ { \circ }$ 
B)  $35.76 ^ { \circ }$ 
C)  $46.08 ^ { \circ }$ 
D)  $1.79 ^ { \circ }$ 
E)  $31.25 ^ { \circ }$ 
A)  $43.92 ^ { \circ }$ 
B)  $35.76 ^ { \circ }$ 
C)  $46.08 ^ { \circ }$ 
D)  $1.79 ^ { \circ }$ 
E)  $31.25 ^ { \circ }$

Question 11

Find $\mathbf { u } \times \mathbf { v }$.
$$\mathbf { u } = \langle - 1 , - 2,1 \rangle , \mathbf { v } = \langle - 8 , - 1 , - 8 \rangle$$

Accepted Answer

A)  $\langle 17 , - 16 , - 15 \rangle$ 
B)  2 
C)  $- 2$ 
D)  $\langle 17,16 , - 15 \rangle$ 
E)  $\langle 8,2 , - 8 \rangle$ 
A)  $\langle 17 , - 16 , - 15 \rangle$ 
B)  2 
C)  $- 2$ 
D)  $\langle 17,16 , - 15 \rangle$ 
E)  $\langle 8,2 , - 8 \rangle$

Question 12

Find the coordinates of the point located five units in front of the $y z$-plane, seven units to the right of the $x z$-plane, and nine units below the $x y$-plane.

Accepted Answer

A)  $( 5 , - 9,7 )$ 
B)  $( 5,7 , - 9 )$ 
C)  $( 5 , - 7 , - 9 )$ 
D)  $( 5 , - 9 , - 7 )$ 
E)  $( 5,12,3 )$ 
A)  $( 5 , - 9,7 )$ 
B)  $( 5,7 , - 9 )$ 
C)  $( 5 , - 7 , - 9 )$ 
D)  $( 5 , - 9 , - 7 )$ 
E)  $( 5,12,3 )$

Question 13

Find a set of symmetric equations of the line that passes through the points $( 3,0,3 )$ and $( 7,4 , - 2 )$.

Accepted Answer

A)  $\frac { x } { 7 } = \frac { y } { 4 } = \frac { z } { - 2 }$ 
B)  $\frac { x - 3 } { 4 } = \frac { y - 4 } { 4 } = \frac { z - 2 } { - 5 }$ 
C)  $\frac { x - 3 } { - 4 } = \frac { y } { 4 } = \frac { z - 3 } { 5 }$ 
D)  $\frac { x + 4 } { 3 } = y - 4 = \frac { z - 5 } { 3 }$ 
E)  $\frac { x - 3 } { 4 } = \frac { y } { 4 } = \frac { z - 3 } { - 5 }$ 
A)  $\frac { x } { 7 } = \frac { y } { 4 } = \frac { z } { - 2 }$ 
B)  $\frac { x - 3 } { 4 } = \frac { y - 4 } { 4 } = \frac { z - 2 } { - 5 }$ 
C)  $\frac { x - 3 } { - 4 } = \frac { y } { 4 } = \frac { z - 3 } { 5 }$ 
D)  $\frac { x + 4 } { 3 } = y - 4 = \frac { z - 5 } { 3 }$ 
E)  $\frac { x - 3 } { 4 } = \frac { y } { 4 } = \frac { z - 3 } { - 5 }$

Question 14

Find the magnitude of the vector described below.
Initial point: $( 5,6 , - 4 )$
Terminal point: $( - 4,2,7 )$

Accepted Answer

A)  2 
B)  36 
C)  $2 \sqrt { 6 }$ 
D)  $2 \sqrt { 218 }$ 
E)  $\sqrt { 218 }$ 
A)  2 
B)  36 
C)  $2 \sqrt { 6 }$ 
D)  $2 \sqrt { 218 }$ 
E)  $\sqrt { 218 }$

Question 15

Find the area of the parallelogram formed by the points $A ( 2 , - 3,5 ) , B ( 8 , - 2,7 )$, $C ( 3 , - 2,8 )$, and $D ( 9 , - 1,10 )$.

Accepted Answer

A)  282 
B)  $\sqrt { 10 }$ 
C)  10 
D)  $\sqrt { 282 }$ 
E)  13 
A)  282 
B)  $\sqrt { 10 }$ 
C)  10 
D)  $\sqrt { 282 }$ 
E)  13

Question 16

Find the general form of the equation of the plane passing through the point and perpendicular to the specified line.
$x = 2 + 3 t$
$( 5 , - 6 , - 4 ) , \quad y = - 3 + 4 t$
$z = - 6 + 6 t$

Accepted Answer

A)  $3 x + 4 y + 6 z = 0$ 
B)  $3 x + 4 y + 6 z - 33 = 0$ 
C)  $3 x + 4 y + 6 z + 33 = 0$ 
D)  $5 x - 6 y - 4 z - 33 = 0$ 
E)  $5 x - 6 y - 4 z + 33 = 0$ 
A)  $3 x + 4 y + 6 z = 0$ 
B)  $3 x + 4 y + 6 z - 33 = 0$ 
C)  $3 x + 4 y + 6 z + 33 = 0$ 
D)  $5 x - 6 y - 4 z - 33 = 0$ 
E)  $5 x - 6 y - 4 z + 33 = 0$

Question 17

Find symmetric equations for the line through the point and parallel to the specified line. Show all your work.
$$x = - 1 - 3 t$$
$( - 6 , - 2,5 )$, parallel to
$$\begin{array} { l } 
y = 6 - 8 t \
z = 4 - 3 t
\end{array}$$

Accepted Answer

Answers may vary. On

Question 18

Find the midpoint of the line segment joining the points.
$$( - 2 , - 7,3 ) , ( - 3 , - 4 , - 6 )$$

Accepted Answer

A)  $\left( \frac { 1 } { 2 } , \frac { - 3 } { 2 } , \frac { 9 } { 2 } \right)$ 
B)  $\left( \frac { - 5 } { 2 } , \frac { - 11 } { 2 } , \frac { - 3 } { 2 } \right)$ 
C)  $( - 5 , - 11 , - 3 )$ 
D)  $( 1 , - 3,9 )$ 
E)  $( 6,28 , - 18 )$ 
A)  $\left( \frac { 1 } { 2 } , \frac { - 3 } { 2 } , \frac { 9 } { 2 } \right)$ 
B)  $\left( \frac { - 5 } { 2 } , \frac { - 11 } { 2 } , \frac { - 3 } { 2 } \right)$ 
C)  $( - 5 , - 11 , - 3 )$ 
D)  $( 1 , - 3,9 )$ 
E)  $( 6,28 , - 18 )$

Question 19

Find the angle between the two planes in degrees. Round to a tenth of a degree.
$$\begin{array} { l } 
x + 2 y + 6 z = 0 \
- 4 x - y - 3 z = 0
\end{array}$$

Accepted Answer

A)  $10.8 ^ { \circ }$ 
B)  $47.3 ^ { \circ }$ 
C)  $137.3 ^ { \circ }$ 
D)  $36.3 ^ { \circ }$ 
E)  $2.4 ^ { \circ }$ 
A)  $10.8 ^ { \circ }$ 
B)  $47.3 ^ { \circ }$ 
C)  $137.3 ^ { \circ }$ 
D)  $36.3 ^ { \circ }$ 
E)  $2.4 ^ { \circ }$

Question 20

Find a set of parametric equations for the line through the point and parallel to the specified vector. Show all your work.
$( - 1 , - 5,9 )$, parallel to $\langle - 7,6 , - 3 \rangle$

Accepted Answer

Answers may vary. On

Determine the values of $c$ such that $\| c \mathbf { u } \| = 6$ , where $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } - 5 \mathbf { k }$ .

Find the standard form of the equation of the sphere with the given characteristics. Endpoints of a diameter: $( - 8,4 , - 2 ) , ( - 8 , - 2,6 )$

Find the volume of the parallelpiped with the given vertices. $A ( 8 , - 5 , - 4 ) , B ( 2,2,5 ) , C ( 9,4 , - 12 ) , D ( 3,11 , - 3 )$ , $E ( 8 , - 6 , - 10 ) , F ( 2,1 , - 1 ) , G ( 9,3 , - 18 ) , H ( 3,10 , - 9 )$

Find the cross product of the unit vectors $k \times i$ .

Find a set of parametric equations for the line that passes through the given points. Show all your work. $\left( 4 , \frac { 9 } { 2 } , \frac { - 3 } { 2 } \right) , \left( \frac { 1 } { 2 } , \frac { - 3 } { 2 } , - 2 \right)$

Find the coordinates of the point located three units in front of the $y z$ -plane, eight units to the right of the $x z$ -plane, and five units above the $x y$ -plane.

Find a set of parametric equations for the line that passes through the given points. Show all your work. $( 9,8 , - 2 ) , ( - 3 , - 6,4 )$

Find the vector $\mathbf { z }$ , given $\mathbf { u } = \langle - 4,9,8 \rangle , \mathbf { v } = \langle 5,4,4 \rangle$ , and $\mathbf { w } = \langle - 3,23,4 \rangle$ . $3 \mathbf { u } - \mathbf { v } + 2 \mathbf { z } = \mathbf { w }$

Find the magnitude of the vector $\mathbf { v }$ . $\mathbf { v } = \langle 0 , - 4 , - 4 \rangle$

Find the acute interior angle of the parallelogram formed by $A ( 2 , - 2,2 )$ , $B ( 5 , - 1,4 ) , C ( 6,0,10 )$ , and $D ( 3 , - 1,8 )$ . Round your answer to two decimals.

Find $\mathbf { u } \times \mathbf { v }$ . $\mathbf { u } = \langle - 1 , - 2,1 \rangle , \mathbf { v } = \langle - 8 , - 1 , - 8 \rangle$

Find the coordinates of the point located five units in front of the $y z$ -plane, seven units to the right of the $x z$ -plane, and nine units below the $x y$ -plane.

Find a set of symmetric equations of the line that passes through the points $( 3,0,3 )$ and $( 7,4 , - 2 )$ .

Find the magnitude of the vector described below. Initial point: $( 5,6 , - 4 )$ Terminal point: $( - 4,2,7 )$

Find the area of the parallelogram formed by the points $A ( 2 , - 3,5 ) , B ( 8 , - 2,7 )$ , $C ( 3 , - 2,8 )$ , and $D ( 9 , - 1,10 )$ .

Find the general form of the equation of the plane passing through the point and perpendicular to the specified line. $x = 2 + 3 t$ $( 5 , - 6 , - 4 ) , \quad y = - 3 + 4 t$ $z = - 6 + 6 t$

Find symmetric equations for the line through the point and parallel to the specified line. Show all your work. $x = - 1 - 3 t$ $( - 6 , - 2,5 )$ , parallel to y=6-8t z=4-3t

Find the midpoint of the line segment joining the points. $( - 2 , - 7,3 ) , ( - 3 , - 4 , - 6 )$

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

Find a set of parametric equations for the line through the point and parallel to the specified vector. Show all your work. $( - 1 , - 5,9 )$ , parallel to $\langle - 7,6 , - 3 \rangle$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

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Limits and an Introduction to Calculus

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Exam 10: Analytic Geometry in Three Dimensions

Determine the values of ccc such that ∥cu∥=6\| c \mathbf { u } \| = 6∥cu∥=6 , where u=−3i+2j−5k\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } - 5 \mathbf { k }u=−3i+2j−5k .

Find the standard form of the equation of the sphere with the given characteristics. Endpoints of a diameter: (−8,4,−2),(−8,−2,6)( - 8,4 , - 2 ) , ( - 8 , - 2,6 )(−8,4,−2),(−8,−2,6)

Find the cross product of the unit vectors k×ik \times ik×i .

Find a set of parametric equations for the line that passes through the given points. Show all your work. (4,92,−32),(12,−32,−2)\left( 4 , \frac { 9 } { 2 } , \frac { - 3 } { 2 } \right) , \left( \frac { 1 } { 2 } , \frac { - 3 } { 2 } , - 2 \right)(4,29​,2−3​),(21​,2−3​,−2)

Find the coordinates of the point located three units in front of the yzy zyz -plane, eight units to the right of the xzx zxz -plane, and five units above the xyx yxy -plane.

Find a set of parametric equations for the line that passes through the given points. Show all your work. (9,8,−2),(−3,−6,4)( 9,8 , - 2 ) , ( - 3 , - 6,4 )(9,8,−2),(−3,−6,4)

Find the magnitude of the vector v\mathbf { v }v . v=⟨0,−4,−4⟩\mathbf { v } = \langle 0 , - 4 , - 4 \ranglev=⟨0,−4,−4⟩

Find the acute interior angle of the parallelogram formed by A(2,−2,2)A ( 2 , - 2,2 )A(2,−2,2) , B(5,−1,4),C(6,0,10)B ( 5 , - 1,4 ) , C ( 6,0,10 )B(5,−1,4),C(6,0,10) , and D(3,−1,8)D ( 3 , - 1,8 )D(3,−1,8) . Round your answer to two decimals.

Find u×v\mathbf { u } \times \mathbf { v }u×v . u=⟨−1,−2,1⟩,v=⟨−8,−1,−8⟩\mathbf { u } = \langle - 1 , - 2,1 \rangle , \mathbf { v } = \langle - 8 , - 1 , - 8 \rangleu=⟨−1,−2,1⟩,v=⟨−8,−1,−8⟩

Find the coordinates of the point located five units in front of the yzy zyz -plane, seven units to the right of the xzx zxz -plane, and nine units below the xyx yxy -plane.

Find a set of symmetric equations of the line that passes through the points (3,0,3)( 3,0,3 )(3,0,3) and (7,4,−2)( 7,4 , - 2 )(7,4,−2) .

Find the magnitude of the vector described below. Initial point: (5,6,−4)( 5,6 , - 4 )(5,6,−4) Terminal point: (−4,2,7)( - 4,2,7 )(−4,2,7)

Find the area of the parallelogram formed by the points A(2,−3,5),B(8,−2,7)A ( 2 , - 3,5 ) , B ( 8 , - 2,7 )A(2,−3,5),B(8,−2,7) , C(3,−2,8)C ( 3 , - 2,8 )C(3,−2,8) , and D(9,−1,10)D ( 9 , - 1,10 )D(9,−1,10) .

Find the general form of the equation of the plane passing through the point and perpendicular to the specified line. x=2+3tx = 2 + 3 tx=2+3t (5,−6,−4),y=−3+4t( 5 , - 6 , - 4 ) , \quad y = - 3 + 4 t(5,−6,−4),y=−3+4t z=−6+6tz = - 6 + 6 tz=−6+6t

Find symmetric equations for the line through the point and parallel to the specified line. Show all your work. x=−1−3tx = - 1 - 3 tx=−1−3t (−6,−2,5)( - 6 , - 2,5 )(−6,−2,5) , parallel to y=6-8t z=4-3t

Find the midpoint of the line segment joining the points. (−2,−7,3),(−3,−4,−6)( - 2 , - 7,3 ) , ( - 3 , - 4 , - 6 )(−2,−7,3),(−3,−4,−6)

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

Find a set of parametric equations for the line through the point and parallel to the specified vector. Show all your work. (−1,−5,9)( - 1 , - 5,9 )(−1,−5,9) , parallel to ⟨−7,6,−3⟩\langle - 7,6 , - 3 \rangle⟨−7,6,−3⟩

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Limits and an Introduction to Calculus

Filters

Determine the values of $c$ such that $\| c \mathbf { u } \| = 6$ , where $\mathbf { u } = - 3 \mathbf { i } + 2 \mathbf { j } - 5 \mathbf { k }$ .

Find the standard form of the equation of the sphere with the given characteristics. Endpoints of a diameter: $( - 8,4 , - 2 ) , ( - 8 , - 2,6 )$

Find the cross product of the unit vectors $k \times i$ .

Find a set of parametric equations for the line that passes through the given points. Show all your work. $\left( 4 , \frac { 9 } { 2 } , \frac { - 3 } { 2 } \right) , \left( \frac { 1 } { 2 } , \frac { - 3 } { 2 } , - 2 \right)$

Find the coordinates of the point located three units in front of the $y z$ -plane, eight units to the right of the $x z$ -plane, and five units above the $x y$ -plane.

Find a set of parametric equations for the line that passes through the given points. Show all your work. $( 9,8 , - 2 ) , ( - 3 , - 6,4 )$

Find the magnitude of the vector $\mathbf { v }$ . $\mathbf { v } = \langle 0 , - 4 , - 4 \rangle$

Find the acute interior angle of the parallelogram formed by $A ( 2 , - 2,2 )$ , $B ( 5 , - 1,4 ) , C ( 6,0,10 )$ , and $D ( 3 , - 1,8 )$ . Round your answer to two decimals.

Find $\mathbf { u } \times \mathbf { v }$ . $\mathbf { u } = \langle - 1 , - 2,1 \rangle , \mathbf { v } = \langle - 8 , - 1 , - 8 \rangle$

Find the coordinates of the point located five units in front of the $y z$ -plane, seven units to the right of the $x z$ -plane, and nine units below the $x y$ -plane.

Find a set of symmetric equations of the line that passes through the points $( 3,0,3 )$ and $( 7,4 , - 2 )$ .

Find the magnitude of the vector described below. Initial point: $( 5,6 , - 4 )$ Terminal point: $( - 4,2,7 )$

Find the area of the parallelogram formed by the points $A ( 2 , - 3,5 ) , B ( 8 , - 2,7 )$ , $C ( 3 , - 2,8 )$ , and $D ( 9 , - 1,10 )$ .

Find the general form of the equation of the plane passing through the point and perpendicular to the specified line. $x = 2 + 3 t$ $( 5 , - 6 , - 4 ) , \quad y = - 3 + 4 t$ $z = - 6 + 6 t$

Find symmetric equations for the line through the point and parallel to the specified line. Show all your work. $x = - 1 - 3 t$ $( - 6 , - 2,5 )$ , parallel to y=6-8t z=4-3t

Find the midpoint of the line segment joining the points. $( - 2 , - 7,3 ) , ( - 3 , - 4 , - 6 )$

Find a set of parametric equations for the line through the point and parallel to the specified vector. Show all your work. $( - 1 , - 5,9 )$ , parallel to $\langle - 7,6 , - 3 \rangle$