courses › Linear Algebra

Dot products, lengths, perpendicular vectors, cross products.

Pen and paper is fine · no calculator needed why?

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Opens at level 35.

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Builds on: Systems of equations (not open yet) · Pythagoras & coordinates (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Dot product par 16 s not tried yet

  worked example

  What is (2, −5, 6) · (6, 0, −3)?

  Answer: -6

  1. Multiply matching entries: 2 × 6, (−5) × 0, 6 × (−3).
  2. Add the products: 12 + 0 − 18 = −6.

• Length of a vector par 13 s not tried yet

  worked example

  What is the length of the vector (6, 7, 6)?

  Answer: 11

  1. Length = √(sum of the squares of the entries).
  2. √(6² + 7² + 6²) = √(36 + 49 + 36) = √121 = 11.

• Perpendicular vectors par 20 s not tried yet

  worked example

  For what value of k are (5, 5) and (−5, k) perpendicular?

  Answer: 5

  1. Perpendicular means the dot product is 0: 5 × (−5) + 5 × k = 0.
  2. That is −25 + 5k = 0, so k = 5.

• Cross product par 30 s not tried yet

  worked example

  What is the y-component of (1, 1, 2) × (4, −3, −4)?

  Answer: 12

  1. With a = (1, 1, 2) and b = (4, −3, −4), the y-component of a × b is a₃b₁ − a₁b₃.
  2. 2 × 4 − 1 × (−4) = 8 − (−4) = 12.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

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