Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b).

Given that a = 5i + 4j and b = 3i + 7j, evaluate (3a - 8b).

Answer Details

To evaluate (3a - 8b), we need to multiply each component of the vectors by their respective scalar, and then add the corresponding components. So, 3a = 3(5i + 4j) = 15i + 12j 8b = 8(3i + 7j) = 24i + 56j Therefore, (3a - 8b) = (15i + 12j) - (24i + 56j) = (-9i - 44j) Hence, the correct answer is option (C) -9i - 44j.