Vectors

Scalars have only magnitude (mass =

Scalars have only magnitude (mass = 50 kg, temperature = 30°C), while vectors have both magnitude and direction (displacement = 10 m east, velocity =

Vectors are represented as directed line

Vectors are represented as directed line segments AB⃗ with magnitude |AB⃗|. Key types: Zero vector (0⃗, magnitude = 0), Unit vector (magnitude = 1), E

Triangle Law

Triangle Law: AB⃗ + BC⃗ = AC⃗. Parallelogram Law: If vectors a⃗ and b⃗ form adjacent sides of parallelogram, their sum is the diagonal. Example: Addin

Any vector r⃗ can be written

Any vector r⃗ can be written as r⃗ = xî + yĵ + zk̂ where î, ĵ, k̂ are unit vectors along x, y, z axes. Magnitude: |r⃗| = √(x² + y² + z²). Example: If

a⃗ · b⃗ = |a⃗||b⃗|cos θ

a⃗ · b⃗ = |a⃗||b⃗|cos θ where θ is angle between vectors. For component form: (a₁î + a₂ĵ + a₃k̂) · (b₁î + b₂ĵ + b₃k̂) = a₁b₁ + a₂b₂ + a₃b₃. Example: (