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Common Core Standard HSN-VM.B.4 Questions

(+) Add and subtract vectors.

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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〉
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4c
For vectors →v and →w, if one were to find →w-→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 →w would touch the tail of vector →v.
  4. The head of vector →v would touch the tail of vector →w.
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a
For →w and →v, is it true that ||→w+→v|| is NEVER equal to ||→w||+||→v||? Why or why not?
  1. Yes this is true. Since the magnitude of a vector involves taking a square root, and you cannot distribute a square root over multiple terms, this can never be true.
  2. Yes this is true. For example, let →u=〈5,2〉 and →v=〈2,3〉.
  3. No, this is not true; there are times when they are equal. Looking at the vectors geometrically, and applying the law of cosines (where the sides are the magnitudes of the vectors), it can be proved that the magnitude of the sums of the vectors are in certain cases equal to the sum of the magnitudes (using some trigonometric identities).
  4. No, this is not true; there are times when they are equal. For example, let →u=〈0,2〉 and →v=〈0,3〉.
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.B.4, HSN-VM.B.4b
If →a has magnitude 21 and direction 55°, and →b has magnitude 15 and direction 320°, what is the magnitude and direction of →a+→b?
  1. Magnitude 22.9, direction 57.8°.
  2. Magnitude 25.3, direction 37.2°.
  3. Magnitude 26.8, direction 357.9°.
  4. Magnitude 24.7, direction 17.8°.
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4b
If →v has magnitude of 8 and direction 200°, and →w has magnitude of 10 and direction 265°, what is the magnitude and direction of →v+→w?
  1. Magnitude 9.8, direction 36.5°.
  2. Magnitude 3.7, direction 163.5°.
  3. Magnitude 15.2, direction 236.5°.
  4. Magnitude 12.2, direction 213.9°.
Grade 11 Vectors CCSS: HSN-VM.A.3, HSN-VM.B.4, HSN-VM.B.4b
Two boats are pulling a very large, derelict boat behind them. One boat is exerting a force of 1.1×106 N on the derelict boat in the direction S10°W. The second boat is pulling with a force of 1.3×106 N in the direction S5°E. What is the resulting force acting on the derelict boat and in what direction? Round answers to the nearest whole unit.
  1. The resulting force is 1.4×106 N, in the direction S7°E.
  2. The resulting force is 2.4×106 N, in the direction S2°W.
  3. The resulting force is 3.7×105 N, in the direction S8°W.
  4. The resulting force is 1.6×106 N, in the direction S2°E.
Grade 11 Vectors CCSS: HSN-VM.B.4, HSN-VM.B.4a
If vector →m=〈-2,4〉 and vector →n=〈6,-8〉, what is the result of →m+→n ?
  1. 〈-6,14〉
  2. 〈-8,12〉
  3. 〈2,-2〉
  4. 〈4,-4〉
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