If A = 1i + 1j + 1k and B = 2i + 2j + 2k, find A · B.

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Question: If A = 1i + 1j + 1k and B = 2i + 2j + 2k, find A · B.

Options:

Correct Answer: 6

Solution:

A · B = (1)(2) + (1)(2) + (1)(2) = 2 + 2 + 2 = 6.

If A = 1i + 1j + 1k and B = 2i + 2j + 2k, find A · B.

If A = 1i + 1j + 1k and B = 2i + 2j + 2k, find A · B.

Step 1: Identify the components of vector A. A = 1i + 1j + 1k means A has components (1, 1, 1).
Step 2: Identify the components of vector B. B = 2i + 2j + 2k means B has components (2, 2, 2).
Step 3: Use the formula for the dot product A · B, which is (A1 * B1) + (A2 * B2) + (A3 * B3).
Step 4: Substitute the components into the formula: (1 * 2) + (1 * 2) + (1 * 2).
Step 5: Calculate each multiplication: 1 * 2 = 2, 1 * 2 = 2, 1 * 2 = 2.
Step 6: Add the results together: 2 + 2 + 2 = 6.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Representation – Understanding how vectors are represented in terms of their components along the i, j, and k axes.