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# Vectors Questions - All Grades

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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.
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
For vectors $vec{v}$ and $vec{w}$, if one were to find $vec{w} - vec{v}$ graphically, which of the following could be true? Choose all that apply.
1. The heads of the vectors would be touching.
2. The tails of the vectors would be touching.
3. The head of vector $vec{w}$ would touch the tail of vector $vec{v}$.
4. The head of vector $vec{v}$ would touch the tail of vector $vec{w}$.
What is the magnitude of a vector with points $(-2,5)$ and $(4,13) ?$
1. $10$
2. $5$
3. $sqrt(7)$
4. $sqrt(14)$
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4b
What is the sum of a vector with magnitude 6 and direction 35° and a vector with magnitude 12 and direction 190°?
1. Magnitude 7.0, direction 168.9°.
2. Magnitude 17.6, direction 133.9°.
3. Magnitude 10.7, direction 135.5°.
4. Magnitude 15.7, direction 170.5°.
What is the magnitude of the vector $<<3,9>> ?$
1. $12$
2. $6sqrt(2)$
3. $3sqrt(10)$
4. $6$
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. $||vec{v}||$
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
For $vec{a} = <<4,8>>, \ \ vec{b} = <<1,7>>$, find the difference, $vec{a} - vec{b}$.
1. $<<-3, 7>>$
2. $<<-4,-6>>$
3. $<<3,1>>$
4. $<<5,15>>$
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4b
If $||vec{n}|| = 2||vec{m}||$, the direction of $vec{n}$ is 40°, and the direction of $vec{m}$ is 160°, in which quadrant does the sum of these vectors lie, and why?
1. Quadrant I, since the resulting direction of the sum of the vectors is 70°.
2. Quadrant I, since the resulting direction of the sum of the vectors is 30°.
3. Quadrant II, since $vec{m}$ is much farther from the positive x-axis than $vec{n}$ (even though $||vec{m}|| < ||vec{n}||$ ).
4. Along the positive y-axis (so not in any quadrant), since the direction of the sum of the vectors is 90°.
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
If you are given $vec{v}$, which of the following is a vector that is twice as long but in the opposite direction?
1. $2vec{v}$
2. $-2vec{v}$
3. $1/2 vec{v}$
4. $-1/2 vec{v}$
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.
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.
Two vectors with the same direction are equal.
1. They are always equal.
2. They are never equal.
3. It depends on their magnitude.
4. It depends on their end point.
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?
2. Yes, they have the same magnitude, $sqrt(41)$.
3. No, because vector $vec{BA}$ does not originate at the origin.
If vector $vec{t} = << 13,28 >>$ and vector $vec{r} = << -13,-28 >>$, what is the result of $vec{t} + vec{r}$ ?
1. $<< -26,-56 >>$
2. $<< 0,0 >>$
3. $<< 26,56 >>$
4. $<< 41,-41 >>$