For vectors A = 2i + 3j and B = 5i + 6j, what is A · B?

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Question: For vectors A = 2i + 3j and B = 5i + 6j, what is A · B?

Options:

Correct Answer: 28

Solution:

A · B = (2)(5) + (3)(6) = 10 + 18 = 28.

For vectors A = 2i + 3j and B = 5i + 6j, what is A · B?

For vectors A = 2i + 3j and B = 5i + 6j, what is A · B?

Step 1: Identify the components of vector A. A = 2i + 3j means A has a component of 2 in the i direction and 3 in the j direction.
Step 2: Identify the components of vector B. B = 5i + 6j means B has a component of 5 in the i direction and 6 in the j direction.
Step 3: Multiply the i components of A and B together. This is (2)(5) = 10.
Step 4: Multiply the j components of A and B together. This is (3)(6) = 18.
Step 5: Add the results from Step 3 and Step 4 together. This is 10 + 18 = 28.
Step 6: The final result of A · B is 28.

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