If A = 3i + 4j and B = 0i + 0j, what is A · B? (2023)

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Question: If A = 3i + 4j and B = 0i + 0j, what is A · B? (2023)

Options:

Correct Answer: 0

Exam Year: 2023

Solution:

A · B = (3)(0) + (4)(0) = 0.

If A = 3i + 4j and B = 0i + 0j, what is A · B? (2023)

If A = 3i + 4j and B = 0i + 0j, what is A · B? (2023)

Step 1: Identify the components of vector A. A = 3i + 4j means A has a component of 3 in the i direction and 4 in the j direction.
Step 2: Identify the components of vector B. B = 0i + 0j means B has a component of 0 in the i direction and 0 in the j direction.
Step 3: Use the formula for the dot product A · B, which is A · B = (A_i * B_i) + (A_j * B_j).
Step 4: Substitute the values into the formula. A_i = 3, B_i = 0, A_j = 4, B_j = 0.
Step 5: Calculate the dot product: A · B = (3 * 0) + (4 * 0).
Step 6: Simplify the calculation: A · B = 0 + 0.
Step 7: Conclude that A · B = 0.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Representation – Vectors can be represented in terms of their components along the i and j axes.