Worked examples: WACE Mathematics Specialist Formula Sheet

Selected worked examples

1. Vectors · angle from a dot product

   Formula or reference: cos θ = (u · v)/(|u||v|).

   Units and conditions: Both vectors must be nonzero. θ is the angle between them.

   Worked example: For u = (1,0,1) and v = (0,1,1), cos θ = 1/2 and θ = 60°.

2. Motion · velocity and acceleration

   Formula or reference: Differentiate position to get velocity and differentiate velocity to get acceleration.

   Units and conditions: If position is in m and time in s, velocity is in m/s and acceleration in m/s².

   Worked example: For r(t) = (3t, t², 0), v(2) = (3,4,0) m/s and a(2) = (0,2,0) m/s².