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

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

Options:

Correct Answer: 0

Solution:

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

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

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

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

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding the individual components of vectors A and B is crucial for correctly applying the dot product formula.