Final answer:
The distance represented by the vector r=t(1,-2,-2) is calculated as the magnitude of the vector, which simplifies to 3t.
Step-by-step explanation:
The question asks about determining the distance represented by a given vector r=t(1,-2,-2). The distance of a vector, also known as its magnitude, can be calculated using the formula \(\sqrt{x^2 + y^2 + z^2}\), where x, y, and z are the components of the vector. In this case, the vector components are proportional to the parameter 't'. Therefore, the distance of the vector r is \(t\sqrt{1^2 + (-2)^2 + (-2)^2}\) which simplifies to \(t\sqrt{1 + 4 + 4}\) = \(t\sqrt{9}\) = 3t.