Geometry Demystified, 2nd edition |

Stan Gibilisco |

Explanations for Quiz Answers in Chapter 9 |

1. On a unit circle in the Cartesian The angle has
a negative value because we must turn clockwise by 60º to get
from the positive cos -60º = 0.500 accurate to three decimal places. The correct choice is A. |

2. On a unit circle in the Cartesian plane, the sin -60º = -0.866 accurate to three decimal places. The answer is D. |

3. When we want to convert an ( and ends at ( When we take the difference between the
When we take the difference between the
Our standard-form vector is (-10,10). The correct choice is B. |

4. You can use the right-hand rule to
determine the direction in which any cross-product vector points (as long
as the two vectors in question don't happen to run off in the same
direction, in which case the cross product equals the zero vector). In
the situation of Fig. 9-14, think of the plane containing vectors
To take advantage of the right-hand
rule, extend your right arm straight out horizontally, turn your hand so
that your palm faces toward your right and the little finger is on
top, and then curl your fingers in a clockwise direction as
viewed from above (from vector |

5. We can calculate the dot product of two vectors by multiplying their
lengths by each other, and then multiplying that result by the cosine of
the angle between them. In the scenario of Fig. 9-14, the angle between
vectors a and b is 90º. Using a calculator (or our memories,
if we've taken any trigonometry courses), we see that cos 90º = 0. The dot
product of these two vectors equals 0. Their lengths don't matter, because
we always end up multiplying the product of the vector lengths by 0. The
answer is A. |

6. Let's refer back to page 224 of the text, where Fig. 9-2 illustrates
the parallelogram method of vector addition. Based on this diagram, we can
envision what happens when we add the vectors in Fig. 9-14: The resultant
sum vector a + b must run off in the plane containing the original
two vectors a and b, and in some direction between them. The
correct choice is C. |

7. When we want to add two vectors in the Cartesian (3,-7) + (6,2) = [(3+6),(-7+2)] The answer is A. |

8. To find the dot product of two vectors in the Cartesian
(3,-7) • (6,2) = (3 x 6) +
(-7 x 2) The correct choice is B. |

9. These two vectors appear in Cartesian 4 and -2 To find the dot product, we multiply the (4 The answer is C. |

10. We can recognize the format of this equation as that of a
plane in Cartesian |