TMJC H2 Chp 6A 3D Vector Geometry (Lines) Learning Package 2024

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Chapter 6A 3D Vector Geometry (Lines) TMJC 2024 Page 1 of 23 H2 Mathematics (9758) Chapter 6A 3D Vector Geometry (Lines) Core Concept Notes Success Criteria: Surface Learning Deep Learning Transfer Learning  Interpret and find equations of lines in the form r = a + d (vector equation) or x a y b z c l m n − − −== (cartesian equation)  Convert the equations from one form to another  Determine the relationship (i.e. intersecting, parallel or skew) between two lines  Explain that two lines are coplanar if they are intersecting or parallel  Find the angle between two lines  Find the point of intersection of two lines if they intersect  Find the length of projection of a vector onto a given line  Find the foot of the perpendicular and perpendicular distance from a point to a line  Find the reflection of a point in a line  Interpret given information in contextual question

Chapter 6A 3D Vector Geometry (Lines) TMJC 2024 Page 2 of 23 Pre Reading Look through the following 2 examples BEFORE the first Independent Learning module on Chapter 6A in SLS. 1. Using the grid, draw the following vectors, marking the points R1, R2, R3, R4 and R5. (a) 1 1 1OR OA =+ − (b) 2 12 1OR OA =+ − (c) 3 13 1OR OA =+ − (d) 4 10 1OR OA =+ − (e) 5 12 1OR OA =− − (i) Join the points R1, R2, R3, R4 and R5. What do they form? (A line segment) (ii) What is the geometrical representation of the following equation? 1 1OR OA  =+ − ,   . Position vector of a point on the line that passes through point A and is parallel to 1 1  − . X 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 O X A X X X X 2R 1R 3R 4R 5R

Chapter 6A 3D Vector Geometry (Lines) TMJC 2024 Page 3 of 23 2. The position vector of any point from the line is given in the form r = ac bd    +       , where   . (i) State 2 possible values of a b   . Just provide the column vector of ANY point on the line. Possible values of a b   are 0 3 6, , etc8 5 2                  (ii) State 2 possible values of c d   . What does d c represent? Possible values of c d   are 11 or 11 −       −    . d c represents the gradient of the straight line. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 O