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Vectors Questions - All Grades

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Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
For vectors [math]vec{v}[/math] and [math]vec{w}[/math], if one were to find [math]vec{w} - vec{v}[/math] 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 [math]vec{w}[/math] would touch the tail of vector [math]vec{v}[/math].
  4. The head of vector [math]vec{v}[/math] would touch the tail of vector [math]vec{w}[/math].
Grade 11 Vectors CCSS: HSN-VM.A.1
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.
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4b
If [math]||vec{n}|| = 2||vec{m}||[/math], the direction of [math]vec{n}[/math] is 40°, and the direction of [math]vec{m}[/math] 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 [math]vec{m}[/math] is much farther from the positive x-axis than [math]vec{n}[/math] (even though [math]||vec{m}|| < ||vec{n}||[/math] ).
  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.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°.
Grade 11 Vectors CCSS: HSN-VM.A.1
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.
Grade 11 Vectors CCSS: HSN-VM.A.1
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.
Grade 11 Vectors CCSS: HSN-VM.A.1
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.
Grade 11 Vectors CCSS: HSN-VM.A.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.
Grade 11 Vectors CCSS: HSN-VM.A.1
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]
Grade 11 Vectors CCSS: HSN-VM.A.1
Grade 11 Vectors CCSS: HSN-VM.A.1
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]
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
Which of the following is the additive inverse of [math]vec{v} = <<-4,6>> ?[/math]
  1. [math]<<4,6>>[/math]
  2. [math]<<1/4, -1/6>>[/math]
  3. [math]<<-1/4, 1/6>>[/math]
  4. [math]<<4,-6>>[/math]
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
For [math]vec{a} = <<4,8>>, \ \ vec{b} = <<1,7>>[/math], find the difference, [math]vec{a} - vec{b}[/math].
  1. [math]<<-3, 7>>[/math]
  2. [math]<<-4,-6>>[/math]
  3. [math]<<3,1>>[/math]
  4. [math]<<5,15>>[/math]
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
Which of the following are equivalent to [math]vec{a} - vec{b} ? [/math] Choose all that apply.
  1. [math]vec{a} + (-vec{b})[/math]
  2. [math]vec{b} - vec{a}[/math]
  3. [math]-vec{a} + vec{b}[/math]
  4. [math]-vec{b} + vec{a}[/math]
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