To find the value of k for the plane x + ky + 2z - 9 = 0, which intersects at a 60-degree angle with the plane 2x + 2y - z = 0, one must first determine the normal vectors of both planes. The angle between the planes corresponds to the angle between these normal vectors, which can be calculated using the dot product. The cosine of the angle can be derived from the dot product formula, but it may be necessary to prove that the angle between the planes is indeed the angle between their normals. Additionally, there is concern about whether solutions are being prematurely provided without confirmation from the original poster. Understanding these concepts is crucial for solving the problem effectively.
