If A = (1, 0, -1) and B = (0, 1, 1), what is the scalar product A · B?

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Question: If A = (1, 0, -1) and B = (0, 1, 1), what is the scalar product A · B?

Options:

Correct Answer: 0

Solution:

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

If A = (1, 0, -1) and B = (0, 1, 1), what is the scalar product A · B?

If A = (1, 0, -1) and B = (0, 1, 1), what is the scalar product A · B?

Step 1: Identify the components of vector A, which are (1, 0, -1).
Step 2: Identify the components of vector B, which are (0, 1, 1).
Step 3: Multiply the first component of A (1) by the first component of B (0). This gives 1 * 0 = 0.
Step 4: Multiply the second component of A (0) by the second component of B (1). This gives 0 * 1 = 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: 0 + 0 - 1.
Step 7: Calculate the final result: 0 + 0 - 1 = -1.

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