If A = 4i + 3j and B = 0i + 5j, what is A · B? (2019)

If A = 4i + 3j and B = 0i + 5j, what is A · B? (2019)

Step 1: Identify the components of vector A. A = 4i + 3j means A has a component of 4 in the i direction and 3 in the j direction.
Step 2: Identify the components of vector B. B = 0i + 5j means B has a component of 0 in the i direction and 5 in the j direction.
Step 3: Use the formula for the dot product A · B, which is A · B = (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 * 5).
Step 5: Calculate the first part: 4 * 0 = 0.
Step 6: Calculate the second part: 3 * 5 = 15.
Step 7: Add the results from Step 5 and Step 6: 0 + 15 = 15.
Step 8: Conclude that A · B = 15.

Dot Product – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding how to break down vectors into their i (horizontal) and j (vertical) components is essential for calculating the dot product.