← Maths Extension 2 syllabus

NSWMaths Extension 2

Further Work with Vectors (MEX-V1)

3 dot points across 3 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How are vectors in three dimensions described, how do we find lines and spheres, and how does the scalar product extend to space?

Represent three-dimensional vectors in component form, compute the scalar product and magnitude, and find vector equations of lines and the equation of a sphere
A focused answer to the HSC Maths Extension 2 dot point on 3D vectors. Component form, magnitude, the scalar product and angle between vectors, parametric vector equations of lines, and the equation of a sphere, with verified worked examples.
6 min answer →

How can vector methods prove classical geometric results such as concurrency, midpoint theorems and properties of parallelograms more cleanly than coordinate geometry?

Prove geometric results using vectors, including properties of triangles, parallelograms and the diagonals of quadrilaterals, by expressing points as position vectors
A focused answer to the HSC Maths Extension 2 dot point on vector geometric proofs. Position vectors, the midpoint and section formulas, using parallelism and the scalar product to prove geometric theorems, with verified worked examples.
6 min answer →

How do we resolve one vector along the direction of another, and what do the scalar and vector projections measure geometrically?

Compute the projection of one vector onto another, distinguishing the scalar projection from the vector projection, and resolve a vector into parallel and perpendicular components
A focused answer to the HSC Maths Extension 2 dot point on vector projection. The scalar projection as a signed length, the vector projection formula, resolving a vector into components parallel and perpendicular to another, with verified worked examples.
6 min answer →