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Common Core Standard HSN-VM.B.4a Questions

Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

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Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a
Evaluate. -4,6+-3,4
  1. 2,1
  2. -1,10
  3. -1,2
  4. -7,10
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=2FE
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 right triangle CDE, how is the magnitude of EC related to θ and the length of ¯ED?
  1. ED=||EC||cosθ
  2. ED=||EC||sinθ
  3. ||EC||=EDcosθ
  4. tanθ=||EC||ED
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.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.4, HSN-VM.B.4a

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

Let n=-6,-1,m=10,-10. Find 2m-5n.
  1. 10,25
  2. -10,-25
  3. 50,-15
  4. 16,9
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.
Let a=3ˆi-6ˆj,b=-ˆi+3ˆj. Find 3a+2b.
  1. 7ˆi-3ˆj
  2. 2ˆi-3ˆj
  3. 11ˆi+24ˆj
  4. 7ˆi-12ˆj
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a
For v=3,-5 and w=-2,-1, find v+w.
  1. 5,6
  2. 1,-6
  3. 5,-4
  4. 1,-4
Grade 10 Systems of Equations CCSS: HSN-VM.B.4, HSN-VM.B.4a
Find the sum. 15,-4+3,4
  1. 18,8
  2. 12,8
  3. 18,0
  4. 11,7
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