What is the scalar product of the vectors A = (2, -1, 3) and B = (0, 4, -2)?

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Question: What is the scalar product of the vectors A = (2, -1, 3) and B = (0, 4, -2)?

Options:

Correct Answer: -10

Solution:

A · B = 2*0 + (-1)*4 + 3*(-2) = 0 - 4 - 6 = -10.

What is the scalar product of the vectors A = (2, -1, 3) and B = (0, 4, -2)?

What is the scalar product of the vectors A = (2, -1, 3) and B = (0, 4, -2)?

Step 1: Identify the components of vector A, which are (2, -1, 3).
Step 2: Identify the components of vector B, which are (0, 4, -2).
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 (-1) by the second component of B (4). This gives -1 * 4 = -4.
Step 5: Multiply the third component of A (3) by the third component of B (-2). This gives 3 * -2 = -6.
Step 6: Add the results from Steps 3, 4, and 5 together: 0 + (-4) + (-6).
Step 7: Calculate the sum: 0 - 4 - 6 = -10.

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