TMJC H2 Chp 5 Vectors Learning Package 2024

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Chapter 5 Vectors TMJC 2024 Page 1 of 28 H2 Mathematics (9758) Chapter 5 Vectors Core Concept Notes Success Criteria: Surface Learning Deep Learning Transfer Learning  Identify position vectors, displacement vectors and direction vectors.  Convert a vector in cartesian form x y z i j k into column vector form x y z         .  Express a displacement vector in terms of the position vectors of its end points. (e.g. AB OB OA        )  Carry out addition and subtraction of vectors, multiplication of a vector by a scalar, and interpret these operations in geometrical terms.  Calculate the magnitude of a vector.  Find the unit vector of a given vector.  Determine if 2 given vectors are parallel.  Calculate dot (scalar) product of two vectors in component form.  Find angle between 2 vectors using the definition of dot product cosa b a b .  Calculate cross (vector) product of two vectors in component form.  Find a vector perpendicular to two non-parallel vectors using cross product.  Use of properties of dot and cross product of equal vectors. (i.e. 2 a a a ,  a a 0 )  Find a vector of a specified magnitude that is parallel to a given vector.  Apply ratio theorem to find vectors.  Determine whether three points with given coordinates are collinear.  Determine if 2 given vectors are perpendicular using dot product (i.e. 0a b ).  Find length of projection of a vector a onto a vector b  Find projection vector of a vector a onto a vector b.  Find the perpendicular/shortest distance from a point to a line.  Use cross product to find area of triangle and parallelogram.  Use properties of dot and cross product to solve problems.  Use ratio theorem or collinearity in geometrical applications.  Visualise using a diagram and use vector concepts to solve problems.  Give geometrical interpretation of a b , a b and a b .  Solve vector related questions involving unknowns.

Chapter 5 Vectors TMJC 2024 Page 2 of 28 §1 Introduction to Vectors At the ‘O’ Level, you have learnt about vectors in 2-dimensional space. We will be now exposed to vectors in 3 -dimensional space, which is more realistic since we live in a 3 -dimensional world. All operations in 2-D also apply in 3-D. Basic Vector Operations (3 dimensional) (i) 1 2 1 2 1 2 1 2 1 2 1 2 x x x x y y y y z z z z                               (ii) ,