# Vector Basics

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## Vector Basics Answer Key

1.

Which of the following are examples of vectors? Choose all that apply.

- The velocity of a baseball thrown from fist base to second base.
- The amount of friction force acting against a pulled sled.
- The mass of a zebra.
- 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.

- The line segment [math]JI[/math].
- The line [math]JI[/math].
- The line segment [math]JI[/math], starting at point J.
- 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?

- It is the angle between the vector and the nearest axis.
- It is the angle between the vector and the nearest x-axis (positive or negative).
- It is the angle formed from the positive x-axis, going counter clockwise, to the vector.
- 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.

- [math]|vec{v}|[/math]
- [math]vec{V}[/math]
- [math]\mathbf{vec{v}}[/math]
- [math]||vec{v}||[/math]

5.

What is the direction of the vector [math]<< -3,5>> ?[/math]

- 59°
- 121°
- 31°
- 211°

6.

What is the magnitude of the vector [math]<<3,9>> ?[/math]

- [math]12[/math]
- [math]6sqrt(2)[/math]
- [math]3sqrt(10)[/math]
- [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]

- 218°
- 52°
- 38°
- 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?

- [math]2sqrt(5)[/math]
- [math]5sqrt(2)[/math]
- [math]6[/math]
- [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?

- Yes, since their magnitudes are equal, the vectors are equal.
- Yes, since they share a point, B.
- No, because their directions will be different (unless points A and C are coincident).
- 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?

- Yes, they are formed by the same points.
- Yes, they have the same magnitude, [math]sqrt(41)[/math].
- No, because vector [math]vec{BA}[/math] does not originate at the origin.
- No, because their directions are different.

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