If A = (1, 2) and B = (3, 4), what is the dot product A · B?

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Question: If A = (1, 2) and B = (3, 4), what is the dot product A · B?

Options:

Correct Answer: 10

Solution:

Dot product A · B = 1*3 + 2*4 = 3 + 8 = 11.

If A = (1, 2) and B = (3, 4), what is the dot product A · B?

If A = (1, 2) and B = (3, 4), what is the dot product A · B?

Step 1: Identify the components of vector A. A = (1, 2) means A has two components: 1 and 2.
Step 2: Identify the components of vector B. B = (3, 4) means B has two components: 3 and 4.
Step 3: Multiply the first component of A by the first component of B. This is 1 * 3.
Step 4: Multiply the second component of A by the second component of B. This is 2 * 4.
Step 5: Add the results from Step 3 and Step 4 together. This is (1 * 3) + (2 * 4).
Step 6: Calculate the result of Step 5. This is 3 + 8.
Step 7: The final result is 11, which is the dot product A · B.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.