Step 1: Identify the components of vector A. A = 2i + 2j means A has a component of 2 in the i direction and a component of 2 in the j direction.
Step 2: Identify the components of vector B. B = 2i + 3j means B has a component of 2 in the i direction and a component of 3 in the j direction.
Step 3: Use the formula for the dot product A · B, which is (A_i * B_i) + (A_j * B_j). Here, A_i is the i component of A, A_j is the j component of A, B_i is the i component of B, and B_j is the j component of B.
Step 4: Substitute the values into the formula. A · B = (2 * 2) + (2 * 3).
Step 5: Calculate the first part: 2 * 2 = 4.
Step 6: Calculate the second part: 2 * 3 = 6.
Step 7: Add the results from Step 5 and Step 6: 4 + 6 = 10.
Step 8: The final result of A · B is 10.
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 notation is essential for performing vector operations.
