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

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.