This IB Maths AA AHL Topic 3.18 – Intersections of Lines and Planes resource develops students’ understanding of how lines and planes meet in three-dimensional space. It begins by connecting geometric intersections to systems of linear equations and showing how substitution can be used to find the intersection of a line and a plane. Students learn how the resulting system indicates whether the line intersects the plane at one point, is parallel to the plane, or lies entirely within the plane.

The lesson then explores the possible intersections of two and three planes. Students practise finding the line of intersection of two planes using a free parameter and interpreting systems of three plane equations as having a unique point, a common line, no common solution, or infinitely many solutions. The resource also develops confidence in calculating the acute angle between a line and a plane using a direction vector and normal vector, as well as the angle between two planes using their normal vectors. With clear geometric interpretations, equation-solving strategies, worked examples, optional derivations, practice questions, and fully worked solutions, this resource helps AHL students build strong fluency with intersections and angles in three-dimensional vector geometry in line with IB Mathematics AA expectations.