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QUESTION 1 Describe the given set of points with a

single equation or with a pair of

equations.

The circle in which the plane through the

point (1, 12, -4) perpendicular to the y-axis

meets the sphere of radius 15 centered at

the origin.

x 2 + y2 + z2 = 81 and y = 12

x 2 + y2 + z2 = 144 and

y = 12

x 2 + y2 + z2 = 63 and

y = 12

x 2 + y2 + z2 = 225 and

y = 12

5 points

QUESTION 2 Find v ? u. v=

0

ij

ij and u = 5 points

QUESTION 3 Give a geometric description of the set

of points whose coordinates satisfy the

given conditions.

(x - 3)2 + (y - 9)2 + (z - 3)2 &lt; 1

All points on the lower hemisphere centered at

(3, 9, 3)

All points outside the lower hemisphere centered

at (3, 9, 3)

All points within the lower hemisphere centered at

(3, 9, 3)

No set of points satisfy the given relations.

5 points

QUESTION 4 Describe the given set of points with a

single equation or with a pair of

equations.

The set of points equidistant from the points

(-7, 0, 0) and (6, 0, 0)

x

x

y

y =

&gt;

+

+ -0.5

-7 and x &lt; 6

z = -0.5

z = 0 and - 7&lt;x&lt;6

5 points

QUESTION 5 Describe the given set of points with a

single equation or with a pair of

equations. The circle in which the plane through the

point (5, 2, -6) perpendicular to the x-axis

meets the sphere of radius 13 centered at

the origin.

x2 + y2 + z2 = 169 and

x=5

x2 + y2 + z2 = 169 and

z=5

x2 + y2 + z2 = 144 and

y=5

x2 + y 2 + z2 = 119 and y=5

5 points

QUESTION 6 Give a geometric description of the set

of points whose coordinates satisfy the

given conditions.

x2 + y2 ? 25, z = 7

All points on the cylinder with radius 5 along the z-axis

All points within the parabola x2 + y2 = 25 in the plane z = 7

All points on or outside of the circle x2 + y2 = 25 and in the

plane z = 7

All points on or within the circle x2 + y2 = 25 and in the plane

z=7

5 points

QUESTION 7 Give a geometric description of the set

of points whose coordinates satisfy the

given conditions. x2 + y2 + z2 &gt; 1

All

All

All

All points

points

points

points outside the sphere of radius 1

outside the cylinder with radius 1

in space

on the surface of the cylinder with radius 1

5 points

QUESTION 8 Give a geometric description of the set

of points whose coordinates satisfy the

given conditions.

3 ? y ? 4, 3 ? z ? 4

The line between the points (0, 3, 3) and (0, 4, 4)

The square with corners at (0, 3, 3), (0, 3, 4), (0, 4, 3), and

(0, 4, 4)

The cube located in the first quadrant and with

sides 3 units in length

The infinitely long square prism parallel to the x-axis

5 points

QUESTION 9 Find the length and direction (when

defined) of u × v.

u = 4i + 2j + 8k, v = -i - 2j - 2k 6 ; 180;

6 ; i+

i+

i- k

k

k i+ 180; j k + 5 points

QUESTION 10 Find the angle between u and v in

u = 4i, v = 7i - 4j

1.5

4

1.0

5

1.2

2

0.5

2

5 points

QUESTION 11 Describe the given set of points with a

single equation or with a pair of

equations.

The circle of radius 5 centered at the point

(7, -4, 10) and lying in a plane perpendicular

to the 2

+

= 25 and x = 7

2

(y + 4) + (z - 10)2 = 25 and

2 y+z=6

(y + 4)2 + (z - 10)2 = 25 and x=7

+ 2 + 1 = 25 2 5 points

QUESTION 12 Find the angle between u and v in

u = -2j and v = 3i - 3k

0.0

0

0.2

4

1.5

7

1.8

1

5 points

QUESTION 13 Find the angle between u and v in

u = 7j - 2k, v = 10i - 4j - 7k

1.57

1.64

1.72

-0.15

5 points

QUESTION 14 Find the length and direction (when

defined) of u × v. u = 2i + 2j - k, v = -i + k 3; i+ j- i- j+ i- j+ i+ j- k

3;

k

9;

k

9;

k

5 points

QUESTION 15 Describe the given set of points with a

single equation or with a pair of

equations.

The set of points equidistant from the points

(0, 0, -9) and (0, 0, -3)

z &gt; -9 and z &lt; -3

z = -6

x + y = -6

x + y = 0 and 9 &lt; z &lt; -3

5 points

QUESTION 16 Find the length and direction (when

defined) of u × v. u=- 2 ;- i+ i+ j + k, v = i + j + 2k j- k

8; i- j+ 8; i- j- 2 ; i+ k

k

j- k

5 points QUESTION 17 Find the distance between

points P1 and P2.

P1(-4, 5, 8) and P2(-3, 4, 7)

9

3

2

5 points

QUESTION 18 Find the distance between

points P1 and P2.

P1(-4, 2, 1) and P2(1, -1, -3)

50

25

5 ;

10

5 points

QUESTION 19 Find v ? u.

v = 2i - 6j and u = -4

-30 i + 5j i - 8j (2 - 4 )i - 1j

-30 - 8

-30 +8

5 points

QUESTION 20 Find v ? u. v= and u = ij

0

i

5 points

S AV E A N D S U B M I T

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Jan 30, 2021

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