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Eleventh Grade (Grade 11) Vectors Questions

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Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
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〉
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a
Write →JO as the sum of unit vectors for points J (6,-2) and O (-9, 5).
  1. -3ˆi+3ˆj
  2. -15ˆi+7ˆj
  3. -1ˆi+-11ˆj
  4. 15ˆi+-7ˆj
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
For the vectors →n and →m, ||a →n||=||→m|| for scalar a, where a can be any non-zero real number. Which of the following statements must be true?
  1. The two vectors have the same direction.
  2. The two vectors have the opposite direction.
  3. The ratio of the magnitudes of →m to →n is a to 1.
  4. The two vectors are equal.
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
For vectors →n=6→v and →m=-12→v, which of the following statements are correct? Choose all correct answers.
  1. The vectors have opposite directions.
  2. -2||→n||=||→m||
  3. Both vectors are in the same direction as →v.
  4. The magnitude of →m is twice that of →n.
Grade 11 Vectors CCSS: HSN-VM.B.5, HSN-VM.B.5b
If ||5→u||=15, what is the value of ||→u||?
  1. 3
  2. 5
  3. 10
  4. Not enough information to determine.
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

This question is a part of a group with common instructions. View group »

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

This question is a part of a group with common instructions. View group »

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.B.4, HSN-VM.B.4a

This question is a part of a group with common instructions. View group »

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.A.2

This question is a part of a group with common instructions. View group »

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

This question is a part of a group with common instructions. View group »

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〉
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