Final answer:
The line segments from (0,0,0) to (1,0,1) to (0,1,2) can be represented as a two-part vector journey, and the magnitude of the resultant vector c can be calculated using the standard formula for vector magnitudes.
Step-by-step explanation:
The representation of c, which consists of line segments from (0,0,0) to (1,0,1) and from (1,0,1) to (0,1,2), can be expressed as a two-part journey, each part described by a vector. The first vector, A, represents the segment from (0,0,0) to (1,0,1), and the second vector, B, represents the segment from (1,0,1) to (0,1,2). To determine the length of vector c, we calculate the sum of the vectors A + B and then find the magnitude of the resulting vector. This process involves finding the components of vector c and then applying the formula for the magnitude of a vector, which is √(Cx² + Cy² + C₂²).