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If C = (0, 1, 2) and D = (3, 4, 5), what is C · D?

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Question: If C = (0, 1, 2) and D = (3, 4, 5), what is C · D?

Options:

  1. 10
  2. 11
  3. 12
  4. 13

Correct Answer: 10

Solution: 

C · D = 0*3 + 1*4 + 2*5 = 0 + 4 + 10 = 14.

If C = (0, 1, 2) and D = (3, 4, 5), what is C · D?

Practice Questions

Q1
If C = (0, 1, 2) and D = (3, 4, 5), what is C · D?
  1. 10
  2. 11
  3. 12
  4. 13

Questions & Step-by-Step Solutions

If C = (0, 1, 2) and D = (3, 4, 5), what is C · D?
  • Step 1: Identify the elements in set C, which are 0, 1, and 2.
  • Step 2: Identify the elements in set D, which are 3, 4, and 5.
  • Step 3: Multiply the first element of C (0) by the first element of D (3). This gives 0 * 3 = 0.
  • Step 4: Multiply the second element of C (1) by the second element of D (4). This gives 1 * 4 = 4.
  • Step 5: Multiply the third element of C (2) by the third element of D (5). This gives 2 * 5 = 10.
  • Step 6: Add all the results from Steps 3, 4, and 5 together: 0 + 4 + 10.
  • Step 7: Calculate the total: 0 + 4 + 10 = 14.
  • Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.
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