If A = 6i + 8j and B = 2i + 3j, what is the value of A · B?

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Question: If A = 6i + 8j and B = 2i + 3j, what is the value of A · B?

Options:

Correct Answer: 54

Solution:

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

If A = 6i + 8j and B = 2i + 3j, what is the value of A · B?

If A = 6i + 8j and B = 2i + 3j, what is the value of A · B?

Step 1: Identify the components of vector A. A = 6i + 8j means A has a component of 6 in the i direction and 8 in the j direction.
Step 2: Identify the components of vector B. B = 2i + 3j means B has a component of 2 in the i direction and 3 in the j direction.
Step 3: Multiply the i components of A and B together. This is 6 (from A) times 2 (from B), which equals 12.
Step 4: Multiply the j components of A and B together. This is 8 (from A) times 3 (from B), which equals 24.
Step 5: Add the results from Step 3 and Step 4 together. This is 12 + 24, which equals 36.
Step 6: The final result, A · B, is 36.

Dot Product of Vectors – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.