If A = (1, 1, 1) and B = (2, 2, 2), what is the scalar product A · B?

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Question: If A = (1, 1, 1) and B = (2, 2, 2), what is the scalar product A · B?

Options:

Correct Answer: 6

Solution:

A · B = 1*2 + 1*2 + 1*2 = 2 + 2 + 2 = 6.

If A = (1, 1, 1) and B = (2, 2, 2), what is the scalar product A · B?

If A = (1, 1, 1) and B = (2, 2, 2), what is the scalar product A · B?

Step 1: Identify the components of vector A, which are (1, 1, 1).
Step 2: Identify the components of vector B, which are (2, 2, 2).
Step 3: Multiply the first component of A (1) by the first component of B (2). This gives 1 * 2 = 2.
Step 4: Multiply the second component of A (1) by the second component of B (2). This gives 1 * 2 = 2.
Step 5: Multiply the third component of A (1) by the third component of B (2). This gives 1 * 2 = 2.
Step 6: Add all the results from Steps 3, 4, and 5 together: 2 + 2 + 2 = 6.
Step 7: The scalar product A · B is 6.

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