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# Common Core Standard HSN-VM.A.1 Questions

(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

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What is the magnitude of the vector $<<3,9>> ?$
1. $12$
2. $6sqrt(2)$
3. $3sqrt(10)$
4. $6$
If a given vector, with direction $theta$, is positioned so that its tail is at the origin, how is $theta$ 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.
For vector $vec{v}$, which of the following indicate(s) its magnitude? Choose all correct answers.
1. $|vec{v}|$
2. $vec{V}$
3. $\mathbf{vec{v}}$
4. $||vec{v}||$
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.
Which of the following would correctly describe a vector defined by points J and I? Choose all that apply.
1. The line segment $bar{JI}$.
2. The line $\stackrel{leftrightarrow}{JI}$.
3. The line segment $\bar{JI}$, starting at point J.
4. The line segment $bar{JI}$, heading in a downward-negative direction.
If $|| vec{AB}|| = 8$, and $|| vec{CB}|| = 8$, 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.
If point A is at the origin and point B is located at $(4,5)$, are the vectors $vec{AB}$ and $vec{BA}$ equal? Why or why not?
1. Yes, they are formed by the same points.
2. Yes, they have the same magnitude, $sqrt(41)$.
3. No, because vector $vec{BA}$ does not originate at the origin.
4. No, because their directions are different.
Two vectors with the same magnitude are equal.
1. They are always equal.
2. They are never equal.
3. It depends on their direction.
4. It depends on their initial point.
What is the magnitude of a vector with points $(-2,5)$ and $(4,13) ?$
1. $10$
2. $5$
3. $sqrt(7)$
4. $sqrt(14)$