Serway & Jewett — Vectors: Problem 33

In Figure P3.33, the line segment represents a path from the point with position vector \((5\hat{i} + 3\hat{j})\text{ m}\) to the point with location \((16\hat{i} + 12\hat{j})\text{ m}\). Point Ⓐ is along this path, a fraction \(f\) of the way to the destination. (a) Find the position vector of point Ⓐ in terms of \(f\). (b) Evaluate the expression from part (a) for \(f = 0\). (c) Explain whether the result in part (b) is reasonable. (d) Evaluate the expression from part (a) for \(f = 1\). (e) Explain whether the result in part (d) is reasonable.