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Dot Product and Angle Between Two Vectors (Grades 11-12)

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Dot Product and Angle Between Two Vectors

1. 
Find the dot product of the given vectors.
[math]<< 8,4 >> " & " << -7, -9 >>[/math]
  1. 20
  2. -92
  3. 92
  4. -20
2. 
Find the dot product of [math]vecy[/math] and [math]vecx[/math] if [math]vec y = <<-3, 12>>[/math] and [math]vec x =<<-8, -2>> [/math].
  1. 48
  2. 0
  3. -20
  4. 10
3. 
Find the dot product of the given vectors.
[math]vecu=-veci+5vecj[/math]
[math]vecv=-6veci-2vecj[/math]
  1. 12
  2. -16
  3. 16
  4. -4
4. 
Find the dot product of the given vectors.
[math]vecu=<<3,9>>[/math]
[math]vecv=<<6,5>>[/math]
  1. 63
  2. 27
  3. 23
  4. 57
5. 
Find the angle between the two vectors.
[math]<<3, 6>> " & " <<3, -8>>[/math]
  1. 142.87°
  2. 122.62°
  3. 132.88°
  4. 150.03°
6. 
Find the measure of the angle between the two vectors.
[math]<<-2, 2>>[/math]
[math]<<8, -1>>[/math]
  1. 135.6°
  2. 122.2°
  3. 140.3°
  4. 142.1°
7. 
Find the angle between the two vectors.
[math]vecu=-8vecj[/math]
[math]vecv=-9veci-2vecj[/math]
  1. 77.47°
  2. 86.42°
  3. 74.87°
  4. 68.92°
8. 
Are these two vectors parallel, orthogonal, or neither?
[math]<<4, -9>> " & " <<-9, 4>>[/math]
  1. parallel
  2. orthogonal
  3. neither
9. 
Are these two vectors parallel, orthogonal, or neither?
[math]vec u=-5veci-2vecj[/math]
[math]vecv=-10veci+25vecj[/math]
  1. parallel
  2. orthogonal
  3. neither
10. 
Find the angle between the vectors [math]vec(HE) and vec(HK)[/math].
Coordinate Plane - 5x5 - With Dots
  1. 49.6°
  2. 154.5°
  3. 86.8°
  4. 35.7°

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