If A = (3, -2, 1) and B = (4, 0, -1), what is the value of A · B?

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Question: If A = (3, -2, 1) and B = (4, 0, -1), what is the value of A · B?

Options:

Correct Answer: -1

Solution:

A · B = 3*4 + (-2)*0 + 1*(-1) = 12 + 0 - 1 = 11.

If A = (3, -2, 1) and B = (4, 0, -1), what is the value of A · B?

If A = (3, -2, 1) and B = (4, 0, -1), what is the value of A · B?

Step 1: Identify the components of vector A, which are (3, -2, 1).
Step 2: Identify the components of vector B, which are (4, 0, -1).
Step 3: Multiply the first component of A (3) by the first component of B (4). This gives 3 * 4 = 12.
Step 4: Multiply the second component of A (-2) by the second component of B (0). This gives -2 * 0 = 0.
Step 5: Multiply the third component of A (1) by the third component of B (-1). This gives 1 * -1 = -1.
Step 6: Add the results from Steps 3, 4, and 5 together: 12 + 0 - 1.
Step 7: Calculate the final result: 12 + 0 = 12, then 12 - 1 = 11.

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