# 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

### Vectors

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Vector Applications
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• 21 Lessons
• 84 Topics
• 60 Quizzes