If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?

If u = (1, 2, 3) and v = (4, 5, 6), what is the dot product u · v?

Correct Answer: 32

Step 1: Identify the components of vector u, which are (1, 2, 3).
Step 2: Identify the components of vector v, which are (4, 5, 6).
Step 3: Multiply the first component of u (1) by the first component of v (4). This gives 1 * 4 = 4.
Step 4: Multiply the second component of u (2) by the second component of v (5). This gives 2 * 5 = 10.
Step 5: Multiply the third component of u (3) by the third component of v (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.
Step 8: The dot product u · v is 32.

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