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Unit Vectors definitions

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  • Unit Vectors
    Vectors with a magnitude of one, used to simplify vector representation in the Cartesian coordinate system.
  • Magnitude
    The length or size of a vector, often calculated using the Pythagorean theorem.
  • Direction
    The orientation of a vector in space, often described using angles or unit vectors.
  • Cartesian Coordinate System
    A coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates.
  • Vector Addition
    The process of combining vectors by adding their corresponding components.
  • Components
    The projections of a vector along the axes of a coordinate system, often expressed using unit vectors.
  • i, j, k Notation
    A notation using unit vectors to represent vector components along the x, y, and z axes.
  • Resultant Vector
    The vector sum of two or more vectors, representing the combined effect of the vectors.
  • Graphical Representation
    A method of visualizing vectors using diagrams, often involving grid squares.
  • Trigonometric Functions
    Functions like sine and cosine used to relate the angles and sides of a triangle.
  • Decomposition
    The process of breaking a vector into its component parts along the coordinate axes.
  • Pythagorean Theorem
    A mathematical equation relating the lengths of the sides of a right triangle.
  • Algebraic Representation
    Expressing vectors using equations and unit vectors to specify components.
  • Tip to Tail Method
    A method of vector addition where the tail of one vector is placed at the tip of another.
  • Negative Direction
    The opposite direction along an axis, often indicated by a negative sign in vector notation.