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Vector Basics

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Vector Basics Answer Key

1. 
Which of the following are examples of vectors? Choose all that apply.
  1. The velocity of a baseball thrown from fist base to second base.
  2. The amount of friction force acting against a pulled sled.
  3. The mass of a zebra.
  4. The direction of a car heading from San Francisco to Boston.
2. 
Which of the following would correctly describe a vector defined by points J and I? Choose all that apply.
Coordinate Plane - 5x5 - With Dots
  1. The line segment [math]JI[/math].
  2. The line [math]JI[/math].
  3. The line segment [math]JI[/math], starting at point J.
  4. The line segment [math]JI[/math], heading in a downward-negative direction.
3. 
If a given vector, with direction [math]theta[/math], is positioned so that its tail is at the origin, how is [math]theta[/math] measured with respect to the graph's axis?
  1. It is the angle between the vector and the nearest axis.
  2. It is the angle between the vector and the nearest x-axis (positive or negative).
  3. It is the angle formed from the positive x-axis, going counter clockwise, to the vector.
  4. It is the angle formed from the positive x-axis, going clockwise, to the vector.
4. 
For vector [math]vec{v}[/math], which of the following indicate(s) its magnitude? Choose all correct answers.
  1. [math]|vec{v}|[/math]
  2. [math]vec{V}[/math]
  3. [math]\mathbf{vec{v}}[/math]
  4. [math]||vec{v}||[/math]
5. 
What is the direction of the vector [math]<< -3,5>> ?[/math]
  1. 59°
  2. 121°
  3. 31°
  4. 211°
6. 
What is the magnitude of the vector [math]<<3,9>> ?[/math]
  1. [math]12[/math]
  2. [math]6sqrt(2)[/math]
  3. [math]3sqrt(10)[/math]
  4. [math]6[/math]
7. 
If point A is [math](5,6)[/math] and point B is [math](-2,-3)[/math], what is the direction of [math]vec{AB}?[/math]
  1. 218°
  2. 52°
  3. 38°
  4. 232°
8. 
Vector [math]vec{np}[/math] has endpoints n at [math](-1,-1)[/math] and p at [math](-5,-3)[/math]. What is the magnitude of this vector?
  1. [math]2sqrt(5)[/math]
  2. [math]5sqrt(2)[/math]
  3. [math]6[/math]
  4. [math]-6[/math]
9. 
If [math]|| vec{AB}|| = 8[/math], and [math]|| vec{CB}|| = 8[/math], are these vectors are considered equal? Why or why not?
  1. Yes, since their magnitudes are equal, the vectors are equal.
  2. Yes, since they share a point, B.
  3. No, because their directions will be different (unless points A and C are coincident).
  4. Uncertain, since their directions is unknown.
10. 
If point A is at the origin and point B is located at [math](4,5)[/math], are the vectors [math]vec{AB}[/math] and [math]vec{BA}[/math] equal? Why or why not?
  1. Yes, they are formed by the same points.
  2. Yes, they have the same magnitude, [math]sqrt(41)[/math].
  3. No, because vector [math]vec{BA}[/math] does not originate at the origin.
  4. No, because their directions are different.

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