Mathematical Methods

Scalars are physical quantities described only

Scalars are physical quantities described only by magnitude and unit (like mass = 5 kg, temperature = 30°C, distance = 100 m). Vectors require both ma

Vectors are added using Triangle Law

Vectors are added using Triangle Law (head-to-tail method) or Parallelogram Law. For parallel vectors: R = A + B (same direction) or R = |A - B| (oppo

Any vector can be broken into

Any vector can be broken into rectangular components: V = Vₓî + Vyĵ + Vzk̂ where Vₓ = V cos θₓ, Vy = V cos θy, Vz = V cos θz. In 2D: Vₓ = V cos θ and

A⃗·B⃗ = AB cos θ =

A⃗·B⃗ = AB cos θ = AₓBₓ + AyBy + AzBz. Results in a scalar quantity. Geometric interpretation: A⃗·B⃗ = A × (component of B along A) = B × (component o

A⃗ × B⃗ = AB sin

A⃗ × B⃗ = AB sin θ n̂ where n̂ is unit vector perpendicular to both A⃗ and B⃗ following right-hand rule. In component form: A⃗ × B⃗ = (AyBz - AzBy)î +