Final answer:
To represent a plane curve by a vector-valued function, use parametric equations. For example, a circle of radius 'r' can be represented as r(t) = [r*cos(t), r*sin(t)].
Step-by-step explanation:
To represent a plane curve by a vector-valued function, we can use parametric equations. Let's take an example of a circle of radius 'r' centered at the origin. We can represent this curve using a vector-valued function as r(t) = [r*cos(t), r*sin(t)], where 't' is the parameter that varies and takes values between 0 and 2*pi. The cosine and sine functions provide the x and y coordinates of points on the circle respectively.