Vector Algebra

Scalars have only magnitude (like 5

Scalars have only magnitude (like 5 kg, 10 seconds, 25°C) while vectors have both magnitude and direction (like 20 m/s towards north, 50 N downward fo

Zero vector (magnitude = 0)

Zero vector (magnitude = 0), Unit vector (magnitude = 1), Position vector (from origin to a point), Coinitial vectors (same starting point), Collinear

Triangle Law

Triangle Law: When vectors are placed head-to-tail, their sum is the vector from the tail of first to head of last. Parallelogram Law: Sum of two vect

When a vector a⃗ is multiplied

When a vector a⃗ is multiplied by scalar λ, the result λa⃗ has magnitude |λ||a⃗| and same direction as a⃗ if λ > 0, opposite direction if λ < 0. Unit

Any vector r⃗ can be expressed

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