H2 Chp 6B 3D Vector Geometry (Lines and Planes) Learning Package 2024

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Chapter 6B 3D Vector Geometry TMJC 2024 Page 1 of 28 H2 Mathematics (9758) Chapter 6B 3D Vector Geometry (Lines & Planes) Core Concept Notes Success Criteria: Surface Learning Deep Learning Transfer Learning  Interpret and find equations of planes in the form ax by cz d   or   0  r a n or    r a b c .  Convert equations of planes from one form to another.  Determine whether a line lies in a plane, is parallel to a plane, or intersects a plane.  Find the angle between a line and a plane, and between two planes.  Find the point of intersection of a line and a plane when it exists.  Find foot of the perpendicular from a point to a plane  Find perpendicular distance between a point and a plane, between a line and a plane, and between two planes.  Find the line of intersection and the angle between two non-parallel planes.  Find the reflection of a point in a plane  Interpret given information in contextual question.  Solve 3D vector geometry questions involving unknowns.

Chapter 6B 3D Vector Geometry TMJC 2024 Page 2 of 28 §1 Equation of Planes A plane is a flat, two-dimensional surface that extends infinitely in all directions. Some examples of planes are: In the rest of this section, we will diagrammatise planes in the shape of a parallelogram. 1.1 Vector Equation of a Plane Consider the plane , which contains a given fixed point A, with position vector a. Suppose that the plane  is parallel to the two non-parallel vectors m1 and m2. Let R be a general point on , and r be the position vector of R. Now, OR OA AR  r       Given two non-parallel vectors 1m and 2m on  , any vector on  may be expressed as a linear combination of those two vectors. Hence, AR   may be expressed as a linear combination of 1m and 2m . i.e 1 2AR   m m   . So,  1 2   r a m m , ,  are real parameters. Vector equation of a plane  which contains the point A with position vector a and parallel to the vectors m1 and m2 is given by: 1 2: , where       r a m m  R O a Position vector of a general point on the plane Position vector of a fixed point on the plane and are two non-parallel vectors that are parallel to the