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 = 3i + 4j means B has a component of 3 in the i direction and 4 in the j direction.
Step 3: To find the dot product A · B, use the formula: 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) * (3) + (3) * (4).
Step 5: Calculate the first part: (4) * (3) = 12.
Step 6: Calculate the second part: (3) * (4) = 12.
Step 7: Add the two results together: 12 + 12 = 24.
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 the components of vectors in terms of i and j (unit vectors in the x and y directions) is crucial for performing vector operations.
