If A = 1i + 1j and B = 1i - 1j, what is the scalar product A · B?

If A = 1i + 1j and B = 1i - 1j, what is the scalar product A · B?

Step 1: Identify the components of vector A. A = 1i + 1j means A has a component of 1 in the i direction and 1 in the j direction.
Step 2: Identify the components of vector B. B = 1i - 1j means B has a component of 1 in the i direction and -1 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 = (1 * 1) + (1 * -1).
Step 5: Calculate the first part of the equation: 1 * 1 = 1.
Step 6: Calculate the second part of the equation: 1 * -1 = -1.
Step 7: Add the results from Step 5 and Step 6: 1 + (-1) = 0.
Step 8: Conclude that the scalar product A · B is 0.

Vector Operations – Understanding how to compute the scalar (dot) product of two vectors.
Component-wise Multiplication – Applying the formula for the dot product by multiplying corresponding components of the vectors.