VCE Specialist Mathematics Units 3 and 4 – Vectors

4.1 Vectors
4.2 Vector Applications

In this area of study students cover the arithmetic and algebra of vectors, linear dependence and independence of a set of vectors, proof of geometric results using vectors, vector representation of curves in the plane and vector kinematics in one and two dimensions.

This area of study includes:

Vectors, including:

  • addition and subtraction of vectors and their multiplication by a scalar, and position vectors
  • linear dependence and independence of a set of vectors and geometric interpretation
  • magnitude of a vector, unit vector, and the orthogonal unit vectors \( \vec{i} , \vec{j} \) and \( \vec{k} \)
  • resolution of a vector into rectangular components
  • scalar (dot) product of two vectors, deduction of dot product for \( \vec{i}, \vec{j}, \vec{k} \) system; its use to find scalar and vector resolutes
  • parallel and perpendicular vectors
  • vector proofs of simple geometric results, for example the diagonals of a rhombus are perpendicular, the medians of a triangle are concurrent, the angle subtended by a diameter in a circle is a right angle.

Vector calculus, including:

  • position vector as a function of time \( r(t) \); and sketching the corresponding path given \( r(t) \), including circles, ellipses and hyperbolas in cartesian or parametric forms
  • differentiation and anti-differentiation of a vector function with respect to time and applying vector calculus to motion in a plane including projectile and circular motion.

source – VCE Mathematics Study Design

VCE Specialist Mathematics Units 3 and 4 Courses

VCE Specialist Mathematics Units 3 and 4 Syllabus

Course Content

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Vectors

Vector Applications
Not Enrolled

Course Includes

  • 21 Lessons
  • 84 Topics
  • 60 Quizzes