Revision

Vectors & Resolution — A/L Physics

Aligned with the NIE syllabus

What must I remember about Vectors & Resolution?

Scalar vs Vector Quantities: Scalars possess magnitude only (mass, time, temperature, electric potential, work); Vectors possess magnitude and directional orientation obeying vector addition laws (displacement, velocity, force, electric field).
Vector Addition: Triangle Law, Parallelogram Law: Resultant R = √(P² + Q² + 2PQ cos θ), tan α = (Q sin θ) / (P + Q cos θ).
Resolution of Vectors into Orthogonal Components: Along x-axis: Fx = F cos θ; Along y-axis: Fy = F sin θ; Magnitude F = √(Fx² + Fy²); Direction tan θ = Fy / Fx.
Vector Products: Scalar (Dot) Product: A · B = |A||B| cos θ (returns a scalar; work W = F · s); Vector (Cross) Product: A × B = |A||B| sin θ n̂ (returns perpendicular vector; torque τ = r × F).

Orthogonal Unit Vectors

î · î = ĵ · ĵ = k̂ · k̂ = 1, while î · ĵ = 0; For cross products: î × ĵ = k̂, ĵ × k̂ = î, k̂ × î = ĵ (cyclic), and î × î = 0.
Relative Velocity

Velocity of A relative to B: v_AB = v_A - v_B; solve vectorially using vector triangles or resolved orthogonal components.
Equilibrium of three coplanar concurrent forces

If three forces acting at a point keep it in equilibrium, they can be represented in magnitude and direction by the sides of a closed triangle taken in order (Lami's Theorem: P/sin α = Q/sin β = R/sin γ).

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 1 & Unit 2

Unit 1.5 · Year 1 · Term 1

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