This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Give a parametric representation of the line (D). The line (D) passes through point A(1,2,3) and is directed by the vector u(2, -2, -1). The parametric equations of a line passing through (x_0, y_0, z_0) with direction vector (a, b, c) are: x = x_0 + at \\ y = y_0 + bt \\ z = z_0 + ct Substituting the given values A(1,2,3) and u(2, -2, -1): x = 1 + 2t \\ y = 2 - 2t \\ z = 3 - t where t R. Step 2: Find the relative position of the line (D) with respect to the planes (P), (Q), and (R). The direction vector of line (D) is u(2, -2, -1).