Final answer:
Vectors are quantities that describe both the magnitude and direction of motion, such as displacement and velocity, while scalars describe only the magnitude, like distance and speed. In one-dimensional motion, vector direction can be indicated using signs, whereas two-dimensional motion involves using coordinates to describe direction.
Step-by-step explanation:
When describing motion, it’s important to understand the difference between vectors and scalars. Vectors have both magnitude and direction, while scalars have only magnitude. For example, displacement and velocity are vectors because they describe not only the size of the motion but also the direction in which the motion occurs. On the contrary, distance and speed are scalars because they quantify motion without providing direction. In one-dimensional motion, a vector’s direction is indicated by a plus or minus sign to signify opposing ends of a line, such as forwards or backwards, left or right, and so on.
In a two-dimensional context like horizontal and vertical motion, vectors are resolved into perpendicular components. With two-dimensional vectors, we typically use a coordinate system as a reference frame to define the direction and magnitude more precisely with graphical representations using arrows. In this way, we can analyze motion in a plane, which is how it often occurs in real life. The incorrect statements in the options include that vectors describe speed (they do not, they describe velocity), and that scalars describe direction or motion in two dimensions which is not true.