Calculus homework

Question 1

1.  

Find the length and direction (when defined) of u × v. u = 4i + 2j + 8k, v = -i - 2j - 2k

		180;  i +  k
		180;  i +   j +  k
		6;  i -  k
		6;  i +  k

5 points  

Question 2

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 = 225 and y = 12
		x 2 + y2 + z2 = 63 and y = 12
		x 2 + y2 + z2 = 81 and y = 12
		x 2 + y2 + z2 = 144 and y = 12

5 points  

Question 3

1.  

Find v ∙ u. v = 2i - 6j and u = -4 i + 5j

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

5 points  

Question 4

1.  

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

		No set of points satisfy the given relations.
		All points outside the lower hemisphere centered at (3, 9, 3)
		All points within the lower hemisphere centered at (3, 9, 3)
		All points on the lower hemisphere centered at (3, 9, 3)

5 points  

Question 5

1.  

Find the length and direction (when defined) of u × v. u = -  i +  j + k, v = i + j + 2k

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

5 points  

Question 6

1.  

Find the distance between points P1 and P2.  P1(-4, 2, 1) and P2(1, -1, -3)

		50
		10
		5;
		25

5 points  

Question 7

1.  

Give a geometric description of the set of points whose coordinates satisfy the given conditions. 3 ≤ y ≤ 4, 3 ≤ z ≤ 4

		The infinitely long square prism parallel to the x-axis
		The cube located in the first quadrant and with sides 3 units in length
		The square with corners at (0, 3, 3), (0, 3, 4), (0, 4, 3), and (0, 4, 4)
		The line between the points (0, 3, 3) and (0, 4, 4)

5 points  

Question 8

1.  

Give a geometric description of the set of points whose coordinates satisfy the given conditions. x2 + y2 ≤ 25, z = 7

		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 the cylinder with radius 5 along the z-axis
		All points on or within the circle x2 + y2 = 25 and in the plane z = 7

5 points  

Question 9

1.  

Find the distance between points P1 and P2. P1(-4, 5, 8) and P2(-3, 4, 7)

		3
		2
		9

5 points  

Question 10

1.  

Find v ∙ u. v =  and u = 

		i -  j
		i -  j
		0

5 points  

Question 11

1.  

Find the angle between u and v in radians. u = 4i, v = 7i - 4j

		1.22
		1.54
		0.52
		1.05

5 points  

Question 12

1.  

Find the angle between u and v in radians. u = 7j - 2k, v = 10i - 4j - 7k

		1.57
		1.72
		-0.15
		1.64

5 points  

Question 13

1.  

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 = -0.5
		y + z = -0.5
		y + z = 0 and -7 < x < 6
		x > -7 and x < 6

5 points  

Question 14

1.  

Find the angle between u and v in radians. u = -2j  and v = 3i - 3k

		1.81
		1.57
		0.00
		0.24

5 points  

Question 15

1.  

Give a geometric description of the set of points whose coordinates satisfy the given conditions.  x2 + y2 + z2 > 1

		All points in space
		All points outside the cylinder with radius 1
		All points outside the sphere of radius 1
		All points on the surface of the cylinder with radius 1

5 points  

Question 16

1.  

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 

		(y + 4)2 + (z - 10)2 = 25 and x = 7
		2+ 2+ 1 = 25
		(y + 4)2 + (z - 10)2 = 25 and y + z = 6
		2 + 2 = 25 and x = 7

5 points  

Question 17

1.  

Find v ∙ u. v =  and u = 

		i -  j
		0
		i

5 points  

Question 18

1.  

Find the length and direction (when defined) of u × v. u = 2i + 2j - k, v = -i + k

		9;  i +  j -  k
		3;  i -  j +  k
		9;  i -  j +  k
		3;  i +  j -  k

5 points  

Question 19

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 (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 20

1.  

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 = -6
		x + y = 0 and -9 < z < -3
		z > -9 and z < -3
		x + y = -6

5 points