What is the scalar product of A = 1i + 2j + 3k and B = 4i + 5j + 6k?

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Question: What is the scalar product of A = 1i + 2j + 3k and B = 4i + 5j + 6k?

Options:

Correct Answer: 32

Solution:

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.

What is the scalar product of A = 1i + 2j + 3k and B = 4i + 5j + 6k?

What is the scalar product of A = 1i + 2j + 3k and B = 4i + 5j + 6k?

Step 1: Identify the components of vector A. A = 1i + 2j + 3k means A has components: A_x = 1, A_y = 2, A_z = 3.
Step 2: Identify the components of vector B. B = 4i + 5j + 6k means B has components: B_x = 4, B_y = 5, B_z = 6.
Step 3: Multiply the corresponding components of A and B. Calculate A_x * B_x = 1 * 4 = 4.
Step 4: Calculate A_y * B_y = 2 * 5 = 10.
Step 5: Calculate A_z * B_z = 3 * 6 = 18.
Step 6: Add the results from Steps 3, 4, and 5 together. 4 + 10 + 18 = 32.
Step 7: The final result is the scalar product A · B = 32.

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