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(solution) HI, I need help with another homework related with calculus . im


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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 < 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 =

 

>

 

+

 

+ -0.5

 

-7 and x < 6

 

z = -0.5

 

z = 0 and - 7<x<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 > 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

 

radians.

 

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

 

radians.

 

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

 

radians.

 

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 > -9 and z < -3

 

z = -6

 

x + y = -6

 

x + y = 0 and 9 < z < -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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