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

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

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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.4b
If ||→n||=2||→m||, the direction of →n is 40°, and the direction of →m 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 →m is much farther from the positive x-axis than →n (even though ||→m||<||→n|| ).
  4. Along the positive y-axis (so not in any quadrant), since the direction of the sum of the vectors is 90°.

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