Final answer:
The error in the representation of the product 3(-6) on the number line is that the arrows should be a length of 6, matching the magnitude of -6, and pointing in the negative direction for a total of 18 units. The correct answer is option b.
Step-by-step explanation:
The correct answer is option b. When we represent the product 3(-6) using a number line, we need to ensure that the arrows depicting this calculation respect the rules of vector representation in one-dimensional motion. In this context, the length of each vector (or arrow) must be proportional to the magnitude of the number it is representing. Therefore, since we are multiplying 3 by -6, the arrows should each be of length 6, and since there are three of them, the total length represented should be 18 units in the negative direction, starting from zero. The arrows should indeed be pointing in the negative direction, as the product is a negative number, hence the answer b is the only correct option.
When representing the product 3(-6) using the number line, we start at zero and draw an arrow with a length of 6 in the negative direction. Since we are multiplying by a negative number, the arrow should be pointing in the opposite direction. The length of the arrow represents the magnitude of the product, which is 18. Therefore, the correct representation would show an arrow with a length of 6 pointing to the left.