If A = 2i + 3j and B = 4i + 5j, what is the value of A · B?

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Question: If A = 2i + 3j and B = 4i + 5j, what is the value of A · B?

Options:

Correct Answer: 23

Solution:

A · B = (2)(4) + (3)(5) = 8 + 15 = 23.

If A = 2i + 3j and B = 4i + 5j, what is the value of A · B?

If A = 2i + 3j and B = 4i + 5j, what is the value of 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 = 4i + 5j means B has a component of 4 in the i direction and 5 in the j direction.
Step 3: To find the dot product A · B, multiply the i components of A and B together: (2)(4).
Step 4: Multiply the j components of A and B together: (3)(5).
Step 5: Add the results from Step 3 and Step 4 together: 8 + 15.
Step 6: The final result is 23, which is the value of A · B.

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