If A = 4i - 3j and B = -2i + 5j, what is the scalar product A · B?

If A = 4i - 3j and B = -2i + 5j, what is the scalar product A · B?

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 = -2i + 5j means B has a component of -2 in the i direction and 5 in the j direction.
Step 3: Write down the formula for the scalar product (dot product) of two vectors A and B. 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 = (4 * -2) + (-3 * 5).
Step 5: Calculate the first part of the equation: 4 * -2 = -8.
Step 6: Calculate the second part of the equation: -3 * 5 = -15.
Step 7: Add the results from Step 5 and Step 6: -8 + (-15) = -8 - 15.
Step 8: Simplify the final result: -8 - 15 = -23.

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