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If A = (1, 2, 3) and B = (4, 5, 6), what is the value of A · B?

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Question: If A = (1, 2, 3) and B = (4, 5, 6), what is the value of A · B?

Options:

  1. 32
  2. 30
  3. 28
  4. 26

Correct Answer: 30

Solution: 

A · B = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

If A = (1, 2, 3) and B = (4, 5, 6), what is the value of A · B?

Practice Questions

Q1
If A = (1, 2, 3) and B = (4, 5, 6), what is the value of A · B?
  1. 32
  2. 30
  3. 28
  4. 26

Questions & Step-by-Step Solutions

If A = (1, 2, 3) and B = (4, 5, 6), what is the value of A · B?
Correct Answer: 32
  • Step 1: Identify the elements of vector A, which are 1, 2, and 3.
  • Step 2: Identify the elements of vector B, which are 4, 5, and 6.
  • Step 3: Multiply the first element of A (1) by the first element of B (4). This gives 1 * 4 = 4.
  • Step 4: Multiply the second element of A (2) by the second element of B (5). This gives 2 * 5 = 10.
  • Step 5: Multiply the third element of A (3) by the third element of B (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.
  • Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.
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