Deck 12: Vectors and the Geometry of Space

Question 1

Answer 1

Question 2

Find the standard equation of the sphere with center C and radius r.

Answer 2

D

Question 3

Answer 3

Question 4

Question 5

Question 6

Determine whether the given points are collinear.

A)Not collinear
B)Collinear

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Find the magnitude of the torque about P correct to two decimal places.

Question 14

Suppose you start at the origin, move along the x-axis a distance of units in the positive direction, and then move downward a distance of units.What are the coordinates of your position?

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Find the center and radius of the sphere.

Question 21

Find the midpoint of the line segment joining the given points.

Question 22

Question 23

Find the distance between the planes.

Question 24

Question 25

Plot the given points in a three-dimensional coordinate system.

Question 26

Question 27

Question 28

Question 29

Find the center and the radius of the sphere that has the given equation.

Question 30

Question 31

Question 32

Question 33

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a right triangle, both, or neither.

Question 34

Sketch the plane in a three-dimensional space represented by the equation.

Question 35

Question 36

Question 37

Question 38

Find, correct to the nearest degree, the angle between the planes.

Question 39

Question 40

Question 41

Question 42

Find the midpoint of the line segment joining the given points.

Question 43

Find, correct to the nearest degree, the angle between the planes.

Question 44

Question 45

Question 46

Determine whether the given points are collinear.

Question 47

Find the distance between the planes.

Question 48

Question 49

Reduce the equation to one of the standard forms.

Question 50

Question 51

Find the center and the radius of the sphere that has the given equation.

Question 52

Question 53

Question 54