Question:

Step 1: Since \(α\) and \(β\) are mutually perpendicular unit vectors, \(|α| = |β| = 1\) and \(α \cdot β = 0\). Step 2: Let \(u = rα + rβ + s(α \times β)\), \(v = α + (α \times β)\), and \(w = sα + sβ + t(α \times β)\). Step 3: For coplanarity, the scalar triple product must be zero: \([u v w] = 0\). Step 4: Computing the determinant in the basis \(\{α, β, α \times β\}\): The condition for coplanarity yields a relationship between \(r\), \(s\), and \(t\). Step 5: Solving the coplanarity condition gives \(s = \frac{r + t}{2}\), which is the arithmetic mean of \(r\) and \(t\).