← Maths Extension 1 syllabus

NSWMaths Extension 1

Vectors (ME-V1)

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we use vectors to prove standard geometric results in the plane?

Use vector methods to prove geometric properties, including parallelism, perpendicularity, midpoint and ratio division
A focused answer to the HSC Maths Extension 1 dot point on geometric proofs using vectors. The standard techniques for showing two lines are parallel or perpendicular, the midpoint formula, the section formula, and complete worked proofs.
8 min answer →

How do we represent a line in the plane using vector equations?

Write parametric vector equations of lines and convert between vector and Cartesian forms
A focused answer to the HSC Maths Extension 1 dot point on parametric vector equations of lines. The point-direction form $\mathbf{r} = \mathbf{a} + \lambda \mathbf{d}$ , conversion to Cartesian, intersection of lines, and the use of parametric form for collision and meeting-point problems.
7 min answer →

What is the scalar (dot) product of two vectors, and what does it measure?

Compute the scalar product of two vectors in component or geometric form and use it to find the angle between vectors and test orthogonality
A focused answer to the HSC Maths Extension 1 dot point on the scalar product. The component formula $\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2$ , the geometric formula $|\mathbf{a}| |\mathbf{b}| \cos \theta$ , properties, and use to find angles and test orthogonality.
8 min answer →

How do we add, subtract and scale two-dimensional vectors, and how do we find their magnitudes?

Perform vector arithmetic with vectors in the plane, including component and column-vector notation, and find the magnitude and unit vector
A focused answer to the HSC Maths Extension 1 dot point on vector arithmetic. Component form, addition, subtraction, scalar multiplication, magnitude, unit vectors, and the standard notation conventions, with worked examples.
8 min answer →

How do we find the projection of one vector onto another, and what does it mean geometrically?

Compute the scalar and vector projection of one vector onto another and interpret it geometrically
A focused answer to the HSC Maths Extension 1 dot point on vector projection. The scalar and vector projections, their formulas, geometric interpretation as the component of one vector along another, and applications, with worked examples.
7 min answer →