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Vectors in Component Form definitions

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  • Vector
    An object represented by an arrow in space, characterized by both magnitude and direction.
  • Component Form
    A representation using ordered pairs that indicate how far a vector extends in the x and y directions.
  • Position Vector
    A vector whose initial point is at the origin, showing displacement to a specific point.
  • Initial Point
    The starting location of a vector, from which its direction and length are measured.
  • Terminal Point
    The ending location of a vector, reached from the initial point by following the vector's direction and length.
  • X Component
    The horizontal part of a vector, indicating movement along the x-axis.
  • Y Component
    The vertical part of a vector, indicating movement along the y-axis.
  • Magnitude
    The total length of a vector, calculated as the square root of the sum of the squares of its components.
  • Pythagorean Theorem
    A formula relating the sides of a right triangle, used to determine the magnitude of a vector.
  • Scalar
    A real number used to multiply a vector, affecting its length but not its direction.
  • Scalar Multiplication
    An operation where each component of a vector is multiplied by a real number.
  • Vector Addition
    A process of combining two vectors by adding their corresponding components.
  • Vector Subtraction
    A process of finding the difference between two vectors by subtracting their corresponding components.
  • Tip to Tail Method
    A graphical technique for adding vectors by connecting the tip of one to the tail of another.
  • Resultant Vector
    The vector obtained from adding or subtracting two or more vectors, representing the combined effect.