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If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?

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Question: If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?

Options:

  1. 32
  2. 27
  3. 26
  4. 30

Correct Answer: 27

Solution: 

Dot product u · v = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?

Practice Questions

Q1
If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?
  1. 32
  2. 27
  3. 26
  4. 30

Questions & Step-by-Step Solutions

If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?
Correct Answer: 32
  • Step 1: Identify the components of vector u, which are (1, 2, 3).
  • Step 2: Identify the components of vector v, which are (4, 5, 6).
  • Step 3: Multiply the first component of u (1) by the first component of v (4). This gives 1 * 4 = 4.
  • Step 4: Multiply the second component of u (2) by the second component of v (5). This gives 2 * 5 = 10.
  • Step 5: Multiply the third component of u (3) by the third component of v (6). This gives 3 * 6 = 18.
  • Step 6: Add the results from Steps 3, 4, and 5 together: 4 + 10 + 18.
  • Step 7: Calculate the total: 4 + 10 = 14, then 14 + 18 = 32.
  • Step 8: The dot product u · v is 32.
  • Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.
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