Vectors

What Is a Vector?

A vector is a quantity that has both magnitude (size) and direction. Represented as an arrow or in component form <a, b>.

Vector Notation

• Component form: <a, b> where a is the horizontal and b is the vertical component.
• Magnitude: |v| = √(a² + b²)
• Direction Angle: θ = tan⁻¹(b/a)

Vector Operations

• Addition: <a₁, b₁> + <a₂, b₂> = <a₁+a₂, b₁+b₂>
• Scalar multiplication: k<a, b> = <ka, kb>
• Subtraction: <a₁, b₁> − <a₂, b₂> = <a₁−a₂, b₁−b₂>

Resultant Vector

The sum of two or more vectors is called the resultant. Geometrically, vectors are added tip-to-tail.