Final answer:
The curvature of the plane curve at t = 3 is 0.
Step-by-step explanation:
The curvature of a plane curve at a given value of the parameter can be found using the formula K = |(r''(t) x r'(t))| / |r'(t)|^3, where r(t) is the parametric equation of the curve. In this case, the parametric equation of the curve is r(t) = ti + 3j, and we are given t = 3. Let's find the corresponding values of r'(t) and r''(t) and substitute them into the curvature formula.
Step 1: Find r'(t) and r''(t)
r'(t) = i (the derivative of ti) + 0 (the derivative of 3j) = i
r''(t) = 0 (the derivative of r'(t) in this case) = 0
Step 2: Substitute the values into the curvature formula
K = |(0 x i)| / |i|^3 = 0 / 1^3 = 0
Therefore, the curvature K of the plane curve at t = 3 is 0.