Vectors (A2 Unit 4: Applied Mathematics B) — WJEC A-Level Mathematics
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Vectors (A2 Unit 4: Applied Mathematics B) explained
Three-dimensional vectors model physical forces, particle velocities, and positions in spatial environments (such as aircraft flight paths or naval navigation).
Read the full explanation
When multiple 3D forces act on a body, their resultant is R = ΣF_i = (Σx_i)i + (Σy_i)j + (Σz_i)k. In equilibrium, the resultant vector is zero (R = 0), requiring balance in all three axes. Under Newton's second law, ΣF = ma applies in 3D. Kinematic equations with constant 3D acceleration extend to v = u + at and r = r₀ + ut + ½at². For variable acceleration, calculus applies component-wise: v = dr/dt and a = dv/dt. Candidates compute speed as |v| and distance from origin as |r|.
Your focus
- Solve 3D static equilibrium and dynamic problems by applying ΣF = 0 and ΣF = ma.
- Apply three-dimensional vector kinematics and calculus to model spatial particle trajectories.
- Compute scalar speeds, travel times, and spatial separations from 3D velocity and position vectors.
Vectors (A2 Unit 4: Applied Mathematics B) exam tips
Marking Points
- calculating the resultant of multiple 3D force vectors by summing Cartesian components
- applying Newton's second law ΣF = ma in three dimensions to find acceleration
- applying 3D vector kinematics or calculus to find velocity or position vectors at time t
- calculating speed as the magnitude of the velocity vector |v| = √(v_x² + v_y² + v_z²)
Examiner Tips
- 💡Keep components separated in column vector form: (x, y, z)ᵀ makes 3D calculations clean and error-free.
- 💡If asked for the speed of an aircraft, compute the magnitude of the velocity vector: √(v_x² + v_y² + v_z²).
Common Mistakes
- confusing velocity (a 3D vector) with speed (the scalar magnitude |v|)
- omitting the initial position vector r₀ when calculating position from displacement in 3D