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If I = (1, 2, 3) and J = (3, 2, 1), what is I · J?

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Question: If I = (1, 2, 3) and J = (3, 2, 1), what is I · J?

Options:

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

Correct Answer: 10

Solution: 

I · J = 1*3 + 2*2 + 3*1 = 3 + 4 + 3 = 10.

If I = (1, 2, 3) and J = (3, 2, 1), what is I · J?

Practice Questions

Q1
If I = (1, 2, 3) and J = (3, 2, 1), what is I · J?
  1. 10
  2. 11
  3. 12
  4. 13

Questions & Step-by-Step Solutions

If I = (1, 2, 3) and J = (3, 2, 1), what is I · J?
  • Step 1: Identify the components of vectors I and J. I = (1, 2, 3) and J = (3, 2, 1).
  • Step 2: Multiply the corresponding components of I and J. First, multiply the first components: 1 * 3.
  • Step 3: Next, multiply the second components: 2 * 2.
  • Step 4: Then, multiply the third components: 3 * 1.
  • Step 5: Add the results of the multiplications together: (1 * 3) + (2 * 2) + (3 * 1).
  • Step 6: Calculate the individual products: 1 * 3 = 3, 2 * 2 = 4, and 3 * 1 = 3.
  • Step 7: Add these products together: 3 + 4 + 3.
  • Step 8: The final result is 10.
  • Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.
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