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

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

Step 1: Identify the components of vector A. A = 4i + 3j means A has a component of 4 in the i direction and a component of 3 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: Use the formula for the dot product A · B, which is calculated as (A's i component * B's i component) + (A's j component * B's j component).
Step 4: Substitute the values into the formula: A · B = (4 * 0) + (3 * 0).
Step 5: Calculate the result: (4 * 0) = 0 and (3 * 0) = 0, so A · B = 0 + 0.
Step 6: 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.