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

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

Step 1: Identify the components of vector A. A = 3i - 2j means A has a component of 3 in the i direction and -2 in the j direction.
Step 2: Identify the components of vector B. B = -i + 4j means B has a component of -1 in the i direction and 4 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 = (3 * -1) + (-2 * 4).
Step 5: Calculate the first part of the equation: 3 * -1 = -3.
Step 6: Calculate the second part of the equation: -2 * 4 = -8.
Step 7: Add the results from Step 5 and Step 6: -3 + (-8) = -3 - 8.
Step 8: Simplify the final result: -3 - 8 = -11.

Vector Operations – Understanding how to perform operations on vectors, specifically the scalar (dot) product.
Component-wise Multiplication – Knowing how to multiply corresponding components of vectors and sum the results.