Given A = 2i + 2j and B = 3i + 3j, what is the scalar product A · B?

Given A = 2i + 2j and B = 3i + 3j, what is the scalar product A · B?

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 = 3i + 3j means B has a component of 3 in the i direction and a component of 3 in the j direction.
Step 3: Calculate the scalar product A · B using the formula A · B = (A_i * B_i) + (A_j * B_j).
Step 4: Substitute the values into the formula. A_i = 2, B_i = 3, A_j = 2, B_j = 3.
Step 5: Perform the multiplication for the i components: (2)(3) = 6.
Step 6: Perform the multiplication for the j components: (2)(3) = 6.
Step 7: Add the results from Step 5 and Step 6: 6 + 6 = 12.
Step 8: Conclude that the scalar product A · B is 12.

Vector Operations – Understanding how to perform operations on vectors, specifically the scalar (dot) product.
Scalar Product Calculation – Applying the formula for the scalar product of two vectors, which involves multiplying corresponding components and summing the results.