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Find dot products and perpendicular vectors

Grade 12 math · Fieldbook Learning

Name ______________________ Date __________

Multiply matching components and add. Perpendicular vectors have dot product 0.

  1. Find the dot product ⟨5, 4⟩ · ⟨−4, 1⟩.
  2. Find the dot product ⟨4, −5⟩ · ⟨−4, 3⟩.
  3. Find the dot product ⟨1, −3⟩ · ⟨4, 5⟩.
  4. Find the dot product ⟨−4, −1⟩ · ⟨2, 2⟩.
  5. Find the dot product ⟨1, 9⟩ · ⟨−4, −9⟩.
  6. Find the dot product ⟨−1, 7⟩ · ⟨−7, 7⟩.
  7. Find the dot product ⟨2, 6⟩ · ⟨−4, 9⟩.
  8. Find the dot product ⟨5, 4⟩ · ⟨−6, −7⟩.
  9. Find the dot product ⟨−3, −5, 1⟩ · ⟨1, −2, −4⟩.
  10. Find the dot product ⟨−3, −4, −6⟩ · ⟨6, −3, 6⟩.
  11. Find the dot product ⟨−4, −3, −1⟩ · ⟨−2, 6, −5⟩.
  12. Find the dot product ⟨−5, −4, 1⟩ · ⟨−2, −1, 3⟩.
  13. For what value of k are ⟨3, 3⟩ and ⟨k, −1⟩ perpendicular?
  14. For what value of k are ⟨−4, 4⟩ and ⟨k, −2⟩ perpendicular?
  15. For what value of k are ⟨3, −3⟩ and ⟨k, −5⟩ perpendicular?
  16. For what value of k are ⟨5, 10⟩ and ⟨k, 4⟩ perpendicular?
  17. For what value of k are ⟨9, −9⟩ and ⟨k, 9⟩ perpendicular?
  18. For what value of k are ⟨7, 14⟩ and ⟨k, −5⟩ perpendicular?
  19. For what value of k are ⟨−5, −10⟩ and ⟨k, −7⟩ perpendicular?
  20. For what value of k are ⟨8, −32⟩ and ⟨k, −5⟩ perpendicular?
More free practice: fieldbooklearning.com/practice/grade-12/dot-products/

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8 of these questions as multiple choice, with near-miss wrong answers, ready for Kahoot or Blooket.

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Answer key: Find dot products and perpendicular vectors

  1. -16
  2. -31
  3. -11
  4. -10
  5. -85
  6. 56
  7. 46
  8. -58
  9. 3
  10. -42
  11. -5
  12. 17
  13. 1
  14. -2
  15. -5
  16. -8
  17. 9
  18. 10
  19. 14
  20. -20