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

If A = 2i + 2j and B = 2i - 2j, 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 = 2i - 2j means B has a component of 2 in the i direction and a component of -2 in the j direction.
Step 3: Write down the formula for the scalar product (dot product) of two vectors. The formula is A · B = (A_i * B_i) + (A_j * B_j), where A_i and A_j are the components of A, and B_i and B_j are the components of B.
Step 4: Substitute the components of A and B into the formula. A · B = (2 * 2) + (2 * -2).
Step 5: Calculate the first part: 2 * 2 = 4.
Step 6: Calculate the second part: 2 * -2 = -4.
Step 7: Add the results from Step 5 and Step 6: 4 + (-4) = 0.
Step 8: Conclude that the scalar product A · B is 0.

Vector Operations – Understanding how to perform operations on vectors, specifically the scalar (dot) product.
Component-wise Multiplication – Applying the formula for the dot product by multiplying corresponding components of the vectors.