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Vectors Questions - All Grades

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Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5a
Which of the following is equivalent to 4〈3,-1〉?
  1. 〈12,-4〉
  2. 〈12,-1〉
  3. 〈7,3〉
  4. 〈3,-4〉
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a

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Using in formation from previous questions, the value of ∠2 can also be determined, as given below.

∠2=tan-1(||→FB||sinθ||→FE||+||→FB||cosθ)

Why is the direction given in terms of the angle between →FC and →FE and not between →FC and →FB?
  1. It has to be given relative to the horizontal vector.
  2. It has to be given in relation to a vector that is parallel to one of the axis.
  3. It doesn't matter, since the diagonals of a parallelogram bisect their respective angles.
  4. It doesn't matter, but it is simpler to derive the equation this way given the work already done with finding the magnitude of the vector.
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a

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Considering triangle CDE, how is the magnitude of →EC related to the length of ¯CD and θ?
  1. CD=||→EC||cosθ
  2. CD=||→EC||sinθ
  3. ||→EC||=CDcosθ
  4. tanθ=||→EC||CD
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a

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Considering parallelogram FBCE, and that point D is collinear with points F and E, which of the following is/are true? (There may be more than one correct answer).
  1. ||→FE||+ED=FD
  2. →FB=→EC
  3. ∠CED=θ
  4. →FB+→EC=2→FE
Grade 11 Vectors CCSS: HSN-VM.A.2

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What are the components of →KD?
  1. 〈-1,-7〉
  2. 〈1,-7〉
  3. 〈-5,-1〉
  4. 〈5,1〉
Grade 11 Vectors CCSS: HSN-VM.A.2

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What are the components of →LI?
  1. 〈-8,-7
  2. 〈8,7〉
  3. 〈0,1〉
  4. 〈0,-1〉
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
If vector →v=〈-3,14〉 and vector →w=〈-8,8〉, what is the result of →v-→w ?
  1. 〈-11,22〉
  2. 〈5,6〉
  3. 〈11,0〉
  4. 〈-17,-16〉
Grade 12 Vectors CCSS: HSN-VM.A.2
What are the components of a vector that has an initial point of (105,-302) and a terminal point of (823,119)?
  1. 〈942,-197〉
  2. 〈928,-183〉
  3. 〈718,-183〉
  4. 〈718,421〉
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a
If vector →t=〈13,28〉 and vector →r=〈-13,-28〉, what is the result of →r+→t ?
  1. 〈-26,-56〉
  2. 〈0,0〉
  3. 〈26,56〉
  4. 〈41,-41〉
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