Chapter 03, Concept Question 09

### If Vector F = q(vector V x vector B) and vector V is perpendicular to vector B, then what is the direction of vector B in the three situations shown in the figure?

(a) Situation (1), *q* positive:

+x

(b) Situation (1), *q* negative:

-x

(c) Situation (2), *q* positive:

+z

(d) Situation (2), *q* negative:

-z

(e) Situation (3), *q* positive:

+z

(f) Situation (3), *q* negative:

-z
Chapter 03, Concept Question 10

The figure shows vector A and four other vectors that have the same magnitude but differ in orientation.

###
(a) Which pairs of those other four vectors have the same dot product with vector A?

(b) Which of those other four vectors have a negative dot product with vector A?

Chapter 03, Concept Question 11

In a game held within a threedimensional maze, you must move your game piece from *start*, at *xyz* coordinates (0, 0, 0), to *finish*, at coordinates (-2 cm, 4 cm, -4 cm). The game piece can undergo only the displacements (in centimeters) given below. If, along the way, the game piece lands at coordinates (-5 cm, -1 cm,-1 cm) or (5 cm, 2 cm,-1 cm), you lose the game. Which displacements and in what sequence will get your game piece to *finish*?

### Chapter 03, Concept Question 12

The *x* and *y* components of four vectors a,b,c, and d are given below. For which vectors will your calculator give you the correct angle *θ *when you use it to find *θ* with tan*θ* =ay/ax? Answer first by examining the figure below, and then check your answers with your calculator.

a_{x} = 3 |
a_{y} = 3 |
c_{x} = -3 |
c_{y}= -3 |

b_{x} = -3 |
b_{y} = 3 |
d_{x} = 3 |
d_{y} = -3 |

Chapter 03, Concept Question 13

Which of the following are correct (meaningful) vector expressions?