VECTORS

Vectors are mathematical entities that have both magnitude (size) and direction, commonly represented as arrows in space. They are used to model physical quantities like force, velocity, and displacement. A vector is often denoted as v = (v₁, v₂, …, vₙ) in n-dimensional space. Key vector operations include:

• Addition: Combining two vectors u and v results in u + v, obtained by adding corresponding components.
• Subtraction: u − v is computed by subtracting components of v from u.
• Scalar Multiplication: Multiplying a vector v by a scalar c scales its magnitude, yielding c · v.
• Dot Product: u · v produces a scalar, measuring the vectors' alignment.
• Cross Product: In 3D, u × v yields a vector perpendicular to both u and v.

These operations are fundamental in physics, engineering, and computer graphics.