If A = 3i + 4j and B = 0i + 0j, what is the scalar product A · B?

If A = 3i + 4j and B = 0i + 0j, what is the scalar product A · B?

Step 1: Identify the components of vector A. A = 3i + 4j means A has a component of 3 in the i direction and a component of 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 a component of 0 in the j direction.
Step 3: Write the formula for the scalar product (dot product) of two vectors. The formula is A · B = (A_i * B_i) + (A_j * B_j), where A_i and A_j are the components of A, and B_i and B_j are the components of B.
Step 4: Substitute the values into the formula. A · B = (3 * 0) + (4 * 0).
Step 5: Calculate the products. 3 * 0 = 0 and 4 * 0 = 0.
Step 6: Add the results from Step 5. 0 + 0 = 0.
Step 7: Conclude that the scalar product A · B is 0.

Vector Operations – Understanding the scalar (dot) product of vectors, which involves multiplying corresponding components and summing the results.
Zero Vector – Recognizing that the scalar product with a zero vector results in zero, regardless of the other vector.