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Unit Vectors and i & j Notation definitions

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  • Vector
    A mathematical quantity described by both magnitude and direction, often represented graphically as an arrow.
  • Magnitude
    The length or size of a vector, calculated using the square root of the sum of squared components.
  • Direction
    The orientation in space that a vector points, indicated by its components or unit vector form.
  • Unit Vector
    A vector with a magnitude of 1, used to indicate direction without affecting size.
  • Scalar
    A quantity described only by magnitude, lacking any directional information.
  • Component Form
    A representation of a vector using its x and y values, typically written as (x, y).
  • I Notation
    A symbolic representation for the unit vector in the x direction, often written as I hat.
  • J Notation
    A symbolic representation for the unit vector in the y direction, often written as J hat.
  • Vector Addition
    A process of combining vectors by summing their corresponding components.
  • Vector Subtraction
    A process of finding the difference between vectors by subtracting their corresponding components.
  • Resultant Vector
    The outcome of adding or subtracting vectors, representing the combined effect.
  • Tip-to-Tail Method
    A graphical technique for combining vectors by connecting the tail of one to the tip of another.
  • X Component
    The horizontal value in a vector's component form, indicating movement along the x axis.
  • Y Component
    The vertical value in a vector's component form, indicating movement along the y axis.
  • Normalization
    The process of converting a vector to a unit vector by dividing each component by its magnitude.