Final answer:
Multiplying a vector by a positive scalar increases the vector's magnitude while the direction remains unchanged. For a vector with components (4,2) multiplied by 9, it becomes (36,18), with a greater magnitude but the same direction.
Step-by-step explanation:
When a vector with components (4,2) is multiplied by the scalar 9, we obtain a new vector (36,18). The rules for scalar multiplication of vectors state that when vector A is multiplied by a scalar c, the magnitude of the product is given by cA. If c is positive, the direction of the product points in the same direction as A; if c is negative, the direction of the product points in the opposite direction as A. Since 9 is positive, the magnitude of the vector increases by a factor of 9, while the direction remains the same. Therefore, the correct answer to the student's question is: A. Magnitude increases, direction remains the same.