If A = (2, 3, 4) and B = (1, 0, -1), find the scalar product A · B.

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Question: If A = (2, 3, 4) and B = (1, 0, -1), find the scalar product A · B.

Options:

Correct Answer: -1

Solution:

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

If A = (2, 3, 4) and B = (1, 0, -1), find the scalar product A · B.

If A = (2, 3, 4) and B = (1, 0, -1), find the scalar product A · B.

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

Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying corresponding components and summing the results.